Sharp Calculator EL 9400 User Manual

Graphing Calculator

EL-9650/9600c/9450/9400

Handbook Vol. 1

Algebra

EL-9650

EL-9450

Download from Www.Somanuals.com. All Manuals Search And Download.

Read this first

1 . Always read “Before Starting”

The key operations of the set up condition are written in “Before Starting” in each section.

It is essential to follow the instructions in order to display the screens as they appear in the

handbook.

2. Set Up Condition

As key operations for this handbook are conducted from the initial condition, reset all memories to the

initial condition beforehand.

2nd F OPTION

Note: Since all memories will be deleted, it is advised to use the CE-LK1P PC link kit (sold

separately) to back up any programmes not to be erased, or to return the settings to the initial

condition (cf. 3. Initial Settings below) and to erase the data of the function to be used.

•

To delete a single data, press 2nd F

Other keys to delete data:

and select data to be deleted from the menu.

OPTION

to erase equations and remove error displays

to cancel previous function

2nd F QUIT

3. Initial settings

Initial settings are as follows:

✩

Format

Stat Plot

Set up

(

Rad, FloatPt, 9, Rect, Decimal(Real), Equation

RectCoord, OFF, OFF, Connect, Sequen

2. PlotOFF

2. INITIAL

5. Default

1. PmtEnd

SET UP

2nd F

✩

2nd F FORMAT

✩

STATPLOT

2nd F

✩✩

Shade

✩✩

Zoom

✩✩

Period

2nd F DRAW

ZOOM

2nd F

FINANCE

✩

Note:

returns to the default setting in the following operation.

(

)

2nd F

ENTER

OPTION

4. Using the keys

Press to use secondary functions (in yellow).

2nd F

To select “sin^-1”:

Press to use the alphabet keys (in blue).

Displayed as follows:

sin^-1

2nd F

ALPHA

2nd F sin

✩

ALPHA

To select A:

Displayed as follows:

sin

ALPHA

✩

5. Notes

•

Some features are provided only on the EL-9650/9600c and not on the EL-9450/9400. (Substi-

tution, Solver, Matrix, Tool etc.)

As this handbook is only an example of how to use the EL-9650/9600c and 9450/9400,

please refer to the manual for further details.

Download from Www.Somanuals.com. All Manuals Search And Download.

Using this Handbook

This handbook was produced for practical application of the SHARP EL-9650/9600c and

EL-9450/9400 Graphing Calculator based on exercise examples received from teachers

actively engaged in teaching. It can be used with minimal preparation in a variety of

situations such as classroom presentations, and also as a self-study reference book.

Notes

EL-9650/9600c Graphing Calculator

Introduction

Explains the process of each

Slope and Intercept of Quadratic Equations

Explanation of the section

A quadratic equation of y in terms of x can be expressed by the standard form y = a (x -h)²

step in the key operations

k, where

is the coefficient of the second degree term

(

y = ax²

c) and ( h, k) is the

vertex of the parabola formed by the quadratic equation. An equation where the largest

exponent on the independent variable x is 2 is considered a quadratic equation. In graphing

quadratic equations on the calculator, let the x- variable be represented by the horizontal

axis and let

be represented by the vertical axis. The graph can be adjusted by varying the

coefficients a, h, and k.

Example

Ex a m p le

EL-9650/9600c Graphing Calculator

Graph various quadratic equations and check the relation between the graphs and

the values of coefficients of the equations.

Example of a problem to be

solved in the section

Ste p

Ke y O p e ra tio n

Disp la

N o te s

y = x²and y = (x-2)².

*Use either pen touch or cursor to operate.

2. ^Graphy = x²and y = x²+2.

3. ^GG^rra^app^hh y = x²and y = 2x²

x²+2.

-1

Change the equation in Y2 to

4. Graph y = x²and y = -2x²

2nd

SUB

ENTER

There may be differences in the results of

Sta r tin g Return all settings to the default value and delete all da

graph plotting depending on the setting.

^calculations2

^ataⁿ.^d-2 View both graphs.

Notice that the addition of

moves

Be fo re

As the Substitution feature is only available on the EL-9650/9600c, this section does not apply to the EL-9450/9400.

the basic

=x²graph up two units

an d th e addition of -2 moves th e

b asic grap h d o w n t w o u n it s o n

the y-axis. This demonstrates the

GRAPH

Before Starting

Ste p

Ke y O p e ra tio n

Disp la

N o te s

*Use either pen touch or cursor to operate.

fact that adding

h)²K will move the basic graph up K units and placing

(<0) will move the basic graph down K units on the axis.

(>0) within the standard form

Important notes to read

before operating the calculator

Enter the equation y = x²for Y1.

x²

θ/

T/n

Change the equation in Y2 to

2x².

-2

Enter the equation y = (x-2)²for Y2

2nd

SUB

ENTER

using Sub feature.

ENTER

View both graphs.

Notice that the multiplication of

pinches or closes the basic

y=x²graph. This demonstrates

ALPHA

ENTER

Step & Key Operation

A clear step-by-step guide

to solving the problems

GRAPH

2nd

SUB

ENTER

the fact that multiplying an

(> 1) in the standard form y =

(

)

will pinch or close

the basic graph.

Notice that the addition of -2

within the quadratic operation

moves the basic

right two units (adding 2 moves

it left two units) on the x-axis.

View both graphs.

-3

=x²graph

GRAPH

-1

Change the equation in Y2 to

y = -2x²

This shows that placing an

(>0) within the standard

form (x - h)²k will move t_Sh_Ue_Bbasic graph right

units and placing an

(

)

(<0²ⁿ)^dwill move it left

units

2-1

on the x-axis.

ENTER

-2

View both graphs.

Notice that the multiplication of

-2 pinches or closes the basic

y =x²graph and flips it (reflects

it) across the x-axis. This dem-

onstrates the fact that multiply-

Display

GRAPH

Illustrations of the calculator

screen for each step

ing an

(<-1) in the standard form

(x - h) ²

will pinch or close the basic graph and flip it (reflect

it) across the x-axis.

The EL-9650/9600c/9450/9400 allows various quadratic equations to be graphed

easily. Also the characteristics of quadratic equations can be visually shown

through the relationship between the changes of coefficient values and their

graphs, using the Substitution feature.

Merits of Using the EL-9650/9600c/9450/9400

Highlights the main functions of the calculator relevant

to the section

2-1

•

When you see the sign on the key:

means same series of key strokes can be done with screen touch on the EL-9650/9600c.

(

: for the corresponding key;

: for the corresponding keys underlined.)

Key operations may also be carried out with the cursor (not shown).

X/ /T/n

•

Different key appearance for the EL-9450/9400: for example

✩

X T

We would like to express our deepest gratitude to all the teachers whose cooperation we received in editing this

book. We aim to produce a handbook which is more replete and useful to everyone, so any comments or ideas

on exercises will be welcomed.

(Use the attached blank sheet to create and contribute your own mathematical problems.)

Thanks to Dr. David P. Lawrence at Southwestern Oklahoma State University for the use of his

teaching resource book (Applying Pre-Algebra/ Algebra using the SHARP EL-9650/ 9600c Graphing

Calculator).

Other books available:

Graphing Calculator EL-9450/ 9400 TEACHERS’ GUIDE

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Slope and Intercept of Linear Equations

A linear equation of y in terms of x can be expressed by the slope-intercept form y = mx+b,

where m is the slope and b is the y- intercept. We call this equation a linear equation since its

graph is a straight line. Equations where the exponents on the x and y are 1 (implied) are

considered linear equations. In graphing linear equations on the calculator, we will let the x

variable be represented by the horizontal axis and let y be represented by the vertical axis.

Ex a m p le

Draw graphs of two equations by changing the slope or the y- intercept.

1. Graph the equations y = x and y = 2x.

2. Graph the equations y = x and y = x.

3. Graph the equations y = x and y = - x.

4. Graph the equations y = x and y = x + 2.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

1-1 Enter the equation y = x for Y1

and y = 2x for Y2.

X/ /T/

X/ /T/n

ENTER

View both graphs.

The equation Y1 = x is dis-

played first, followed by the

equation Y2 = 2x. Notice how

Y2 becomes steeper or climbs

faster. Increase the size of the

slope (m>1) to make the line

steeper.

1-2

GRAPH

2-1

2-2

Enter the equation y = x for Y2.

X/ /T/

View both graphs.

Notice how Y2 becomes less

steep or climbs slower. De-

crease the size of the slope

(0<m<1) to make the line less

steep.

GRAPH

1-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Enter the equation y = - x for Y2.

3-1

3-2

( )

X/ /T/

View both graphs.

Notice how Y2 decreases

(going down from left to

right) instead of increasing

(going up from left to right).

Negative slopes (m<0) make

the line decrease or go

GRAPH

down from left to right.

4-1

4-2

Enter the equation y = x + 2 for

Y2.

X/ /T/n

View both graphs.

Adding 2 will shift the y = x

graph upwards.

GRAPH

Making a graph is easy, and quick comparison of several graphs will help

students understand the characteristics of linear equations.

1-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Parallel and Perpendicular Lines

Parallel and perpendicular lines can be drawn by changing the slope of the linear equation

and the y intercept. A linear equation of y in terms of x can be expressed by the slope-

intercept form y = mx + b, where m is the slope and b is the y-intercept.

Parallel lines have an equal slope with different y-intercepts. Perpendicular lines have

slopes that are negative reciprocals of each other (m = - ). These characteristics can be

verified by graphing these lines.

Ex a m p le

Graph parallel lines and perpendicular lines.

1. Graph the equations y = 3x + 1 and y = 3x + 2.

2. Graph the equations y = 3x - 1 and y = - x + 1.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Set the zoom to the decimal window:

(

)

ZOOM

ENTER ALPHA

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Enter the equations y = 3x + 1 for

Y1 and y = 3x + 2 for Y2.

1-1

1-2

X/ /T/n

ENTER

X/ /T/n

View the graphs.

These lines have an equal

slope but different y-intercepts.

They are called parallel, and

will not intersect.

GRAPH

2-1

Enter the equations y = 3x - 1 for

Y1 and y = - x + 1 for Y2.

—

X/ /T/

ENTER

( )

X/ /T/n

1-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

View the graphs.

2-2

These lines have slopes that

are negative reciprocals of

GRAPH

each other (m = - ). They are

called perpendicular. Note that

these intersecting lines form

four equal angles.

The Graphing Calculators can be used to draw parallel or perpendicular

lines while learning the slope or y-intercept of linear equations.

1-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Slope and Intercept of Quadratic Equations

A quadratic equation of y in terms of x can be expressed by the standard form y = a (x - h) ²+ k,

where a is the coefficient of the second degree term (y = ax ²+ bx + c) and (h, k) is the

vertex of the parabola formed by the quadratic equation. An equation where the largest

exponent on the independent variable x is 2 is considered a quadratic equation. In graphing

quadratic equations on the calculator, let the x-variable be represented by the horizontal

axis and let y be represented by the vertical axis. The graph can be adjusted by varying the

coefficients a, h, and k.

Ex a m p le

Graph various quadratic equations and check the relation between the graphs and

the values of coefficients of the equations.

1. Graph y = x ²and y = (x - 2) ².

2. Graph y = x ²and y = x ²+ 2.

3. Graph y = x ²and y = 2x ².

4. Graph y = x ²and y = -2x ².

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

*Use either pen touch or cursor to operate.

Disp la y

N o te s

Enter the equation y = x²for Y1.

1-1

1-2

x²

X/ /T/n

Enter the equation y = (x - 2)²for

Y2 using Sub feature.

ENTER

ALPHA

2nd F

ENTER

SUB

ENTER

(

)

ENTER

Notice that the addition of -2

within the quadratic operation

moves the basic y = x graph

View both graphs.

1-3

GRAPH

right two units (adding 2 moves

it left two units) on the x-axis.

This shows that placing an h (>0) within the standard

form y = a (x - h) ²+ k will move the basic graph right

h units and placing an h (<0) will move it left h units

on the x-axis.

2-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

*Use either pen touch or cursor to operate.

²+2.

2-1

2-2

Change the equation in Y2 to y =

2nd F

SUB

ENTER

View both graphs.

Notice that the addition of 2 moves

the basic y = x ²graph up two units

and the addition of - 2 moves the

basic graph down two units on

the y-axis. This demonstrates the

GRAPH

fact that adding k (>0) within the standard form y = a (x -

h) ²+ k will move the basic graph up k units and placing k

(<0) will move the basic graph down k units on the y-axis.

Change the equation in Y2 to y = 2x ²

3-1

3-2

2nd F

ENTER

SUB

ENTER

Notice that the multiplication of

2 pinches or closes the basic

y = x ²graph. This demonstrates

the fact that multiplying an a

(> 1) in the standard form y = a

(x - h) ²+ k will pinch or close

the basic graph.

View both graphs.

GRAPH

4-1

4-2

Change the equation in Y2 to

y = - 2x ².

( )

2nd F

SUB

ENTER

Notice that the multiplication of

-2 pinches or closes the basic

View both graphs.

y =x ²graph and flips it (reflects

GRAPH

it) across the x-axis. This dem-

onstrates the fact that multiply-

ing an a (<-1) in the standard form y = a (x - h) ²+ k

will pinch or close the basic graph and flip it (reflect

it) across the x-axis.

The EL-9650/9600c allows various quadratic equations to be graphed easily.

Also the characteristics of quadratic equations can be visually shown through

the relationship between the changes of coefficient values and their graphs,

using the Substitution feature.

2-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Shifting a Graph of Quadratic Equations

A quadratic equation of y in terms of x can be expressed by the standard form y = a (x - h) ²+ k,

where a is the coefficient of the second degree term (y = ax ²+ bx + c) and (h, k) is the vertex

of the parabola formed by the quadratic equation. An equation where the largest exponent

on the independent variable x is 2 is considered a quadratic equation. In graphing quadratic

equations on the calculator, let the x-variable be represented by the horizontal axis and let y

be represented by the vertical axis. The relation of an equation and its graph can be seen by

moving the graph and checking the coefficients of the equation.

Ex a m p le

Move or pinch a graph of quadratic equation y = x ²to verify the relation between

the coefficients of the equation and the graph.

1. Shift the graph y = x ²upward by 2.

2. Shift the graph y = x ²to the right by 3.

3. Pinch the slope of the graph y = x ².

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

1-1 Access Shift feature and select the

equation y = x ².

2nd F SHIFT/CHANGE

Move the graph y = x ²upward by 2.

1-2

1-3

ENTER

Save the new graph and observe the

changes in the graph and the

equation.

Notice that upward movement

of the basic y = x ²graph by 2

units in the direction of the y-

axis means addition of 2 to the

y-intercept. This demonstrates

ENTER

ALPHA

that upward movement of the graph by k units means

adding a k (>0) in the standard form y = a (x - h) ²+ k.

2-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Move the graph y = x ²to the right by 3.

2-1

2-2

(three times)

ENTER

Save the new graph and observe

the changes in the graph and the

equation

Notice that movement of the

basic y = x²graph to the right

by 3 units in the direction of

the x-axis is equivalent to the

addition of 3 to the x -intercept.

ENTER

ALPHA

This demonstrates that movement of the graph to the

right means adding an h (>0) in the standard form

y = a (x - h) ²+ k and movement to the left means

subtracting an h (<0).

3-1

3-2

Access Change feature and select

the equation y = x ².

2nd F SHIFT/CHANGE

Pinch the slope of the graph.

ENTER

Notice that p inching or

closing the basic y = x²graph

is equivalent to increasing an

a (>1) within the standard

form y = a (x - h) ²+ k and

broadening the grap h is

equivalent to decreasing an

a (<1).

Save the new graph and observe

the changes in the graph and the

equation.

3-3

ENTER

ALPHA

The Shift/Change feature of the EL-9650/9600c/9450/9400 allows visual understanding

of how graph changes affect the form of quadratic equations.

2-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Solving a Literal Equation Using the Equation Method (Amortization)

The Solver mode is used to solve one unknown variable by inputting known variables, by

three methods: Equation, Newton’s, and Graphic. The Equation method is used when an

exact solution can be found by simple substitution.

Ex a m p le

Solve an amortization formula. The solution from various values for known variables

can be easily found by giving values to the known variables using the Equation

method in the Solver mode.

-1

-N

)

1-(1+

P= monthly payment

L= loan amount

I= interest rate

N=number of months

The formula : P = L

I / 12

1. Find the monthly payment on a $15,000 car loan, made at 9% interest over four

years (48 months) using the Equation method.

2. Save the formula as “AMORT”.

3. Find amount of loan possible at 7% interest over 60 months with a $300

payment, using the saved formula.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

*Use either pen touch or cursor to operate.

Disp la y

N o te s

Access the Solver feature.

This screen will appear a few

seconds after “SOLVER” is dis-

played.

1-1

1-2

SOLVER

2nd F

Select the Equation method for

solving.

SOLVER

2nd F

Enter the amortization formula.

1-3

SOLVER

ALPHA

2nd F

(

—

(

ALPHA

)

a^b

( )

ALPHA

a^b

( )

3-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

*Use either pen touch or cursor to operate.

1-4

1-5

Enter the values L=15,000,

I=0.09, N=48.

ENTER

•

ENTER

The monthly payment (P) is

$373.28.

Solve for the payment(P).

2nd F EXE

(

)

2-1

2-2

Save this formula.

2nd F SOLVER

ENTER

Give the formula the name AMORT.

ENTER

Recall the amortization formula.

3-1

3-2

SOLVER

2nd F

Enter the values: P = 300,

I = 0.01, N = 60

ENTER

•

ENTER

The amount of loan (L) is

$17550.28.

Solve for the loan (L).

3-3

2nd F

EXE

With the Equation Editor, the EL-9650/9600c displays equations, even complicated

ones, as they appear in the textbook in easy to understand format. Also it is

easy to find the solution for unknown variables by recalling a stored equation

and giving values to the known variables in the Solver mode when using the

EL-9650/9600c.

3-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Solving a Literal Equation Using the Graphic Method (Volume of a Cylinder)

The Solver mode is used to solve one unknown variable by inputting known variables.

There are three methods: Equation, Newton’s, and Graphic. The Equation method is used

when an exact solution can be found by simple substitution. Newton’s method implements

an iterative approach to find the solution once a starting point is given. When a starting

point is unavailable or multiple solutions are expected, use the Graphic method. This

method plots the left and right sides of the equation and then locates the intersection(s).

Ex a m p le

Use the Graphic method to find the radius of a cylinder giving the range of the unknown

variable.

The formula : V = πr ²h ( V = volume r = radius h = height)

1. Find the radius of a cylinder with a volume of 30in³and a height of 10in, using

the Graphic method.

2. Save the formula as “V CYL”.

3. Find the radius of a cylinder with a volume of 200in ³and a height of 15in,

using the saved formula.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

*Use either pen touch or cursor to operate.

Disp la y

N o te s

Access the Solver feature.

This screen will appear a few

seconds after “SOLVER” is dis-

played.

1-1

2nd F SOLVER

1-2 Select the Graphic method for

solving.

2nd F SOLVER

Enter the formula V = πr ²h.

1-3

1-4

ALPHA

2nd F

ALPHA

x²

ALPHA

Enter the values: V = 30, H = 10.

Solve for the radius (R).

ENTER

2nd F

EXE

3-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

*Use either pen touch or cursor to operate.

Set the variable range from 0 to 2.

1-5

1-6

The graphic solver will prompt

with a variable range for solv-

ing.

ENTER

10π

r ²=

r =1 ➞ r ²= 1²= 1 <3

r =2 ➞ r ²= 2²= 4 >3

Use the larger of the values to

be safe.

The solver feature will graph

the left side of the equation

(volume, y = 30), then the right

side of the equation (y = 10r ²),

and finally will calculate the

intersection of the two graphs

to find the solution.

Solve.

2nd F EXE

(

)

The radius is 0.98 in.

Save this formula.

Give the formula the name “V CYL”.

2nd F SOLVER

ENTER

SPACE

ENTER

Recall the formula.

Enter the values: V = 200, H = 15.

3-1

2nd F SOLVER

ENTER

200

15π

r ²=

< 14

Solve the radius setting the variable

range from 0 to 4.

3-2

r = 3 ➞ r ²= 3²= 9 < 14

r = 4 ➞ r ²= 4²= 16 > 14

2nd F

EXE

ENTER

Use 4, the larger of the values,

to be safe.

The answer is : r = 2.06

One very useful feature of the calculator is its ability to store and recall equations.

The solution from various values for known variables can be easily obtained by

recalling an equation which has been stored and giving values to the known

variables. The Graphic method gives a visual solution by drawing a graph.

3-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Solving a Literal Equation Using Newton's Method (Area of a Trapezoid)

The Solver mode is used to solve one unknown variable by inputting known variables.

There are three methods: Equation, Newton’s, and Graphic. The Newton’s method can

be used for more complicated equations. This method implements an iterative approach

to find the solution once a starting point is given.

Ex a m p le

Find the height of a trapezoid from the formula for calculating the area of a trapezoid

using Newton’s method.

The formula : A= h(b+c)

(A = area h = height b = top face c = bottom face)

1. Find the height of a trapezoid with an area of 25in²and bases of length 5in

and 7in using Newton's method. (Set the starting point to 1.)

2. Save the formula as “A TRAP”.

3. Find the height of a trapezoid with an area of 50in²with bases of 8in and 10in

using the saved formula. (Set the starting point to 1.)

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

Disp la y

N o te s

*Use either pen touch or cursor to operate.

Access the Solver feature.

2nd F SOLVER

1-1

This screen will appear a few

seconds after “SOLVER” is dis-

played.

1-2 Select Newton's method

for solving.

2nd F SOLVER

Enter the formula A = h(b+c).

1-3

1-4

ALPHA

(

ALPHA

)

Enter the values: A = 25, B = 5, C = 7

ENTER

3-3

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

*Use either pen touch or cursor to operate.

Newton's method will

prompt with a guess or a

starting point.

1-5 Solve for the height and enter a

starting point of 1.

2nd F

EXE

ENTER

The answer is : h = 4.17

Solve.

1-6

2nd F EXE

(

)

Save this formula. Give the formula

the name “A TRAP”.

2nd F SOLVER

ENTER

SPACE

ENTER

Recall the formula for calculating

the area of a trapezoid.

3-1

3-2

2nd F SOLVER

Enter the values:

A = 50, B = 8, C = 10.

ENTER

Solve.

The answer is : h = 5.56

3-3

2nd F EXE

ENTER

One very useful feature of the calculator is its ability to store and recall equations.

The solution from various values for known variables can be easily obtained by

recalling an equation which has been stored and giving values to the known

variables in the Solver mode. If a starting point is known, Newton's method is

useful for quick solution of a complicated equation.

3-3

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Graphing Polynomials and Tracing to Find the Roots

A polynomial y = f (x) is an expression of the sums of several terms that contain different

powers of the same originals. The roots are found at the intersection of the x-axis and

the graph, i. e. when y = 0.

Ex a m p le

Draw a graph of a polynomial and approximate the roots by using the Zoom-in

and Trace features.

1. Graph the polynomial y = x ³- 3x ²+ x + 1.

2. Approximate the left-hand root.

3. Approximate the middle root.

4. Approximate the right-hand root.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Set the zoom to the decimal window:

(

)

ZOOM

ENTER ALPHA

ENTER

Setting the zoom factors to 5 :

ZOOM

ENTER

ENTER 2nd F QUIT

Ste p & Ke y O p e ra tio n

*Use either pen touch or cursor to operate.

Disp la y

N o te s

Enter the polynomial

1-1

1-2

y = x ³- 3x ²+ x + 1.

ENTER

Enter the coefficients.

It may take few seconds for

the graph to be drawn.

Enter each coefficients when

2nd F SUB

the cursor is displayed.

ENTER

( )

ENTER

Return to the equation display

screen.

1-3

1-4

2nd F EXE

View the graph.

GRAPH

4-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

*Use either pen touch or cursor to operate.

Tracer

Note that the tracer is flashing

on the curve and the x and y

coordinates are shown at the

bottom of the screen.

2-1

2-2

2-3

Move the tracer near the left-hand

root.

TRACE

(repeatedly)

Zoom in on the left-hand root.

ZOOM

Tracer

Move the tracer to approximate the

root.

The root is : x -0.42

TRACE

(repeatedly)

3-1 Return to the previous decimal

viewing window.

ZOOM

Tracer

Move the tracer to approximate

the middle root.

The root is exactly x = 1.

(Zooming is not needed to

find a better approximate.)

3-2

TRACE

(repeatedly)

Tracer

Move the tracer near the right-

hand root.

The root is : x 2.42

Zoom in and move the tracer to

find a better approximate.

(repeatedly)

ZOOM

TRACE

(repeatedly)

The calculator allows the roots to be found (or approximated) visually by

graphing a polynomial and using the Zoom-in and Trace features.

4-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Graphing Polynomials and Jumping to Find the Roots

A polynomial y = f (x) is an expression of the sums of several terms that contain different

powers of the same originals. The roots are found at the intersection of the x- axis and the

graph, i. e. when y = 0.

Ex a m p le

Draw a graph of a polynomial and find the roots by using the Calculate feature.

1. Graph the polynomial y = x ⁴+ x ³- 5x ²- 3x + 1.

2. Find the four roots one by one.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Setting the zoom factors to 5 :

ZOOM

ENTER

ENTER 2nd F QUIT

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

1-1

Enter the polynomial

y = x ⁴+ x ³- 5x ²- 3x + 1

a^b

X/ /T/n

a^b

—

x²

X/ /T/

X/ /T/n

—

1-2

2-1

View the graph.

GRAPH

Find the first root.

2nd F CALC

-2.47

Y is almost but not exactly zero.

Notice that the root found here

is an approximate value.

Find the next root.

2-2

-0.82

2nd F CALC

4-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Find the next root.

2-3

0.24

2.05

2nd F CALC

2-4 Find the next root.

2nd F CALC

The calculator allows jumping to find the roots by graphing a polynomial

and using the Calculate feature, without tracing the graph.

4-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Solving a System of Equations by Graphing or Tool Feature

A system of equations is made up of two or more equations. The calculator provides the

Calculate feature and Tool feature to solve a system of equations. The Calculate feature

finds the solution by calculating the intersections of the graphs of equations and is useful

for solving a system when there are two variables, while the Tool feature can solve a linear

system with up to six variables and six equations.

Ex a m p le

Solve a system of equations using the Calculate or Tool feature. First, use the Calcu-

late feature. Enter the equations, draw the graph, and find the intersections. Then,

use the Tool feature to solve a system of equations.

1. Solve the system using the Calculate feature.

y = x ²- 1

{

y = 2x

2. Solve the system using the Tool feature.

5x + y = 1

{

-3x + y = -5

There may be differences in the results of calculations and graph plotting depending on the setting.

Be fo re

Sta r tin g

Return all settings to the default and delete all data.

Choose the viewing window “-5 < X < 5”, “-10 < Y < 10” using Rapid window feature

(

)

WINDOW

ENTER

ALPHA

ENTER

As the Tool feature is only available on the EL-9650/9600c, the example 2 does not apply to the EL-9450/9400.

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

1-1 Enter the system of equations

y = x ²- 1 for Y1 and y = 2x for Y2.

X/ /T/

x ²

—

ENTER

X/ /T/

1-2

1-3

1-4

View the graphs.

GRAPH

Note that the x and y coordi-

nates are shown at the bot-

tom of the screen. The answer

is : x = - 0.41 y = - 0.83

The find the left-hand intersection

using the Calculate feature.

2nd F CALC

Find the right-hand intersection by

accessing the Calculate feature again.

The answer is : x = 2.41

y = 4.83

2nd F CALC

5-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Access the Tool menu. Select the

number of variables.

2-1

2-2

Using the system function, it

is possible to solve simulta-

neous linear equations. Sys-

tems up to six variables and

six equations can be solved.

2nd F TOOL

Enter the system of equations.

ENTER

( )

ENTER

2-3

Solve the system.

x = 0.75

y = - 2.75

2nd F EXE

A system of equations can be solved easily by using the Calculate feature

or Tool feature.

5-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Entering and Multiplying Matrices

A matrix is a rectangular array of elements in rows and columns that is treated as a single

element. A matrix is often used for expressing multiple linear equations with multiple

variables.

Ex a m p le

Enter two matrices and execute multiplication of the two.

1. Enter a 3x3 matrix A

1 2 1

2 1 -1

1 1 -2

1 2 3

4 5 6

7 8 9

2. Enter a 3x3 matrix B

3. Multiply the matrices A and B

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

*Use either pen touch or cursor to operate.

Disp la y

N o te s

1-1

1-2

1-3

Access the matrix menu.

MATRIX

Set the dimension of the matrix at

three rows by three columns.

ENTER

Enter the elements of the first row,

the elements of the second row, and

the elements of the third row.

ENTER

( )

ENTER

( )

6-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

*Use either pen touch or cursor to operate.

Enter a 3 x3 matrix B.

MATRIX

ENTER

Matrix multiplication can be

performed if the number of col-

umns of the first matrix is equal

to the number of rows of the

second matrix. The sum of these

Multiply the matrices A and B

together at the home screen.

3-1

MATRIX

ENTER

. . .

multiplications (1 1 + 2 4 + 1 7)

is placed in the 1,1 (first row,

first column) position of the re-

sulting matrix. This process is

repeated until each row of A has

been multiplied by each column

of B.

Delete the input matrices for

future use.

3-2

2nd F

OPTION

ENTER

QUIT

ENTER

2nd F

Matrix multiplication can be performed easily by the calculator.

6-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Solving a System of Linear Equations Using Matrices

Each system of three linear equations consists of three variables. Equations in more than

three variables cannot be graphed on the graphing calculator. The solution of the system of

equations can be found numerically using the Matrix feature or the System solver in the

Tool feature.

A system of linear equations can be expressed as AX = B (A, X and B are matrices). The

-1

solution matrix X is found by multiplying A B. Note that the multiplication is “order sensitive”

-1

and the correct answer will be obtained by multiplying BA . An inverse matrix A is a

-1

matrix that when multiplied by A results in the identity matrix I (A x A=I). The identity

matrix I is defined to be a square matrix (n xn) where each position on the diagonal is 1

and all others are 0.

Ex a m p le

Use matrix multiplication to solve a system of linear equations.

1. Enter the 3x3 identity matrix in matrix A.

1 2 1

2. Find the inverse matrix of the matrix B.

2 1 -1

3. Solve the equation system.

1 1 -2

x + 2y + z = 8

2x + y - z = 1

{

x + y - 2z = -3

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

*Use either pen touch or cursor to operate.

Disp la y

N o te s

Set up 3 x3 identity matrix at the

home screen.

1-1

MATRIX

ENTER

1-2

1-3

Save the identity matrix in matrix A.

MATRIX

ENTER

STO

Confirm that the identity matrix is

stored in matrix A.

MATRIX

6-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

N o te s

Ste p & Ke y O p e ra tio n

Disp la y

*Use either pen touch or cursor to operate.

Enter a 3 x3 matrix B.

2-1

2-2

MATRIX

ENTER

( )

ENTER

( )

Some square matrices have no

inverse and will generate error

statements when calculating the

inverse.

Exit the matrix editor and find the

inverse of the square matrix B.

2nd F QUIT CL

-0.17 0.83 - 0.5

x^-1

MATRIX

2nd F

ENTER

B^-1=

0.5 -0.5

0.5

0.17 0.17 - 0.5

(repeatedly)

The system of equations can be

expressed as

Enter the constants on the right side

of the equal sign into matrix C (3 x1).

3-1

-3

1 2 1

2 1 -1

1 1 -2

MATRIX

ENTER

( )

ENTER

Let each matrix B, X, C :

BX = C

B^-1BX = B^-1C (multiply both

sides by B^-1)

I = B^-1(B^-1B = I, identity matrix)

X = B^-1C

-1

Calculate B C.

3-2

The 1 is the x coordinate, the 2

the y coordinate, and the 3 the z

coordinate of the solution point.

(x, y, z)=(1, 2, 3)

MATRIX

x^-1

MATRIX

2nd F

ENTER

3-3 Delete the input matrices for future

use.

2nd F OPTION

ENTER

2nd F QUIT

The calculator can execute calculation of inverse matrix and matrix

multiplication. A system of linear equations can be solved easily using the

Matrix feature.

6-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Solving Inequalities

To solve an inequality, expressed by the form of f (x)

≤

0, f (x) ≥ 0, or form of f (x)

≤

g(x),

f (x) g(x), means to find all values that make the inequality true.

≥

There are two methods of finding these values for one-variable inequalities, using graphical

techniques. The first method involves rewriting the inequality so that the right-hand side of

the inequality is 0 and the left-hand side is a function of x. For example, to find the solution

to f (x) < 0, determine where the graph of f (x) is below the x-axis. The second method

involves graphing each side of the inequality as an individual function. For example, to find

the solution to f (x) < g(x), determine where the graph of f (x) is below the graph of g(x).

Ex a m p le

Solve an inequality in two methods.

1. Solve 3(4 - 2x)

≥

5 - x, by rewriting the right-hand side of the inequality as 0.

Solve 3(4 - 2x) ≥ 5 - x, by shading the solution region that makes the inequality true.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

*Use either pen touch or cursor to operate.

Disp la y

N o te s

1-1 Rewrite the equation 3(4 - 2x)

≥

5 - x

3(4 - 2x) ≥ 5 - x

so that the right-hand side becomes 0,

and enter y = 3(4 - 2x) - 5 + x for Y1.

(

)

X/ /T/n

—

X/ /T/

View the graph.

1-2

1-3

GRAPH

Find the location of the x-intercept

and solve the inequality.

The x-intercept is located at

the point (1.4, 0).

Since the graph is above the

x-axis to the left of the x-in-

tercept, the solution to the in-

equality 3(4 - 2x) - 5 + x ≥ 0 is

all values of x such that

x ≤ 1.4.

2nd F CALC

7-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

N o te s

*Use either pen touch or cursor to operate.

Enter y = 3(4 - 2x) for Y1 and

y = 5 - x for Y2.

2-1

(7 times)

(4 times)

DEL

X/ /T/n

ENTER

—

2-2

2-3

View the graph.

GRAPH

Access the Set Shade screen.

2nd F DRAW

Since the inequality being

solved is Y1 ≥ Y2, the solu-

tion is where the graph of Y1

is “on the top” and Y2 is “on

the bottom.”

Set up the shading.

2-4

2-5

2-6

—

View the shaded region.

GRAPH

Find where the graphs intersect and

solve the inequality.

The point of intersection is

(1.4, 3.6). Since the shaded

region is to the left of x = 1.4,

the solution to the inequality

3(4 - 2x) ≥ 5 - x is all values

of x such that x ≤ 1.4.

2nd F CALC

Graphical solution methods not only offer instructive visualization of the solution

process, but they can be applied to inequalities that are often difficult to solve

algebraically. The EL-9650/9600c allows the solution region to be indicated visually

using the Shade feature. Also, the points of intersection can be obtained easily.

7-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Solving Double Inequalities

The solution to a system of two inequalities in one variable consists of all values of the variable

that make each inequality in the system true. A system f (x) ≥ a, f (x) ≤ b, where the same expression

appears on both inequalities, is commonly referred to as a “double” inequality and is often written

in the form a ≤ f (x) ≤ b. Be certain that both inequality signs are pointing in the same direction and

that the double inequality is only used to indicate an expression in x “trapped” in between two

values. Also a must be less than or equal to b in the inequality a ≤ f (x) ≤ b or b ≥ f (x) ≥ a.

Ex a m p le

Solve a double inequality, using graphical techniques.

2x - 5 ≥ -1

2x -5 ≤ 7

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

The “double” inequality

given can also be written to

-1 ≤ 2x - 5 ≤ 7.

Enter y = -1 for Y1, y = 2x - 5 for

Y2, and y = 7 for Y3.

( )

ENTER

—

X/ /T/n

ENTER

View the lines.

GRAPH

y = 2x - 5 and

y = -1 intersect at (2, -1).

Find the point of intersection.

2nd F CALC

7-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

y = 2x - 5 and y = 7

intersect at (6,7).

Move the tracer and find another

intersection.

2nd F CALC

Solve the inequalities.

The solution to the “double”

inequality -1 ≤ 2x - 5 ≤ 7 con-

sists of all values of x in be-

tween, and including, 2 and 6

(i.e., x ≥ 2 and x ≤ 6). The so-

lution is 2 ≤ x ≤ 6.

Graphical solution methods not only offer instructive visualization of the solution

process, but they can be applied to inequalities that are often difficult to solve

algebraically. The EL-9650/9600c/9450/9400 allows the solution region to be indicated

visually using the Shade feature. Also, the points of intersection can be obtained easily.

7-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

System of Two-Variable Inequalities

The solution region of a system of two-variable inequalities consists of all points (a, b) such

that when x = a and y = b, all inequalities in the system are true. To solve two-variable

inequalities, the inequalities must be manipulated to isolate the y variable and enter the

other side of the inequality as a function. The calculator will only accept functions of the

form y = . (where y is defined explicitly in terms of x).

Ex a m p le

Solve a system of two-variable inequalities by shading the solution region.

2x + y ≥ 1

x²+ y ≤ 1

There may be differences in the results of calculations and graph plotting depending on the setting.

Sta r tin g Return all settings to the default value and delete all data.

Be fo re

Set the zoom to the decimal window:

(

)

ENTER

ZOOM

2nd F

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

2x + y ≥ 1 © y ≥ 1 - 2x

Rewrite each inequality in the system

so that the left-hand side is y :

x²+ y ≤ 1 © y ≤ 1 - x²

Enter y = 1 - 2x for Y1 and y = 1 - x ²

for Y2.

—

ENTER

X/ /T/n

x²

—

X/ /T/n

Access the set shade screen

2nd F DRAW

Shade the points of y -value so that

Y1 ≤ y ≤ Y2.

—

The intersections are (0, 1)

and (2, -3)

Graph the system and find the

intersections.

GRAPH

2nd F CALC

The solution is 0 ≤ x ≤ 2.

Solve the system.

Graphical solution methods not only offer instructive visualization of the solution process,

but they can be applied to inequalities that are often difficult to solve algebraically.

The EL-9650/9600c/9450/9400 allows the solution region to be indicated visually using

the Shade feature. Also, the points of intersection can be obtained easily.

7-3

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Graphing Solution Region of Inequalities

The solution region of an inequality consists of all points (a, b) such that when x = a, and y = b,

all inequalities are true.

Ex a m p le

Check to see if given points are in the solution region of a system of inequalities.

1. Graph the solution region of a system of inequalities:

x + 2y ≤ 1

x ²+ y ≥ 4

2. Which of the following points are within the solution region?

(-1.6, 1.8), (-2, -5), (2.8, -1.4), (-8,4)

There may be differences in the results of calculations and graph plotting depending on the setting.

Sta r tin g Return all settings to the default value and delete all data.

Be fo re

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

1-x

x + 2y ≤ 1 © y ≤

Rewrite the inequalities so that the

left-hand side is y.

1-1

1-2

x²+y ≥ 4 © y ≥ 4 - x ²

1-x

Enter y =

for Y1 and

y = 4 - x ²for Y2.

X/ /T/n

—

x²

ENTER

X/ /T/n

Set the shade and view the solution

region.

Y2 ≤ y ≤ Y1

1-3

2nd F DRAW

—

GRAPH

Set the display area (window) to :

-9 < x < 3, -6 < y < 5.

2-1

WINDOW

( )

ENTER

( )

ENTER

7-4

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Use the cursor to check the position

of each point. (Zoom in as necessary).

Points in the solution region

are (2.8, -1.4) and (-8, 4).

Points outside the solution

region are (-1.6, 1.8) and

(-2, -5).

2-2

2-3

GRAPH

(-1.6, 1.8): -1.6 + 2 © 1.8 = 2

Substitute p oints and confirm

whether they are in the solution

region.

©©© This does not materialize.

(-2, -5): -2 + 2 © (-5) = -12

(-2)²+ (-5) = -1

©©© This does not materialize.

( )

•

₈...⁺

(2.8, -1.4): 2.8 + 2 © (-1.4) = 0

(2.8)²+ (-1.4) = 6.44

•

©©© This materializes.

(Continuing key operations omitted.)

(-8, 4): -8 + 2 © 4 = 0

(-8)²+ 4 = 68

©©© This materializes.

Graphical solution methods not only offer instructive visualization of the solution process,

but they can be applied to inequalities that are often very difficult to solve algebraically.

The EL-9650/9600c/9450/9400 allows the solution region to be indicated visually using

the Shading feature. Also, the free-moving tracer or Zoom-in feature will allow the

details to be checked visually.

7-4

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Slope and Intercept of Absolute Value Functions

The absolute value of a real number x is defined by the following:

| x| =

x if x ≥ 0

-x if x ≤ 0

If n is a positive number, there are two solutions to the equation | f (x)| = n because there

are exactly two numbers with the absolute value equal to n: n and -n. The existence of two

distinct solutions is clear when the equation is solved graphically.

An absolute value function can be presented as y = a| x - h| + k. The graph moves as the

changes of slope a, x-intercept h, and y-intercept k.

Ex a m p le

Consider various absolute value functions and check the relation between the

graphs and the values of coefficients.

1. Graph y = | x|

2. Graph y = | x -1| and y = | x| -1 using the Rapid Graph feature.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Set the zoom to the decimal window:

(

)

ZOOM

ENTER 2nd F

Ste p & Ke y O p e ra tio n

*Use either pen touch or cursor to operate.

Disp la y

N o te s

1-1

1-2

Enter the function y =| x| for Y1.

MATH

X/ /T/n

Notice that the domain of f(x)

= | x| is the set of all real num-

bers and the range is the set of

non-negative real numbers.

Notice also that the slope of the

graph is 1 in the range of X > 0

and -1 in the range of X ≤ 0.

View the graph.

GRAPH

2-1

Enter the standard form of an abso-

lute value function for Y2 using the

Rapid Graph feature.

ENTER

Substitute the coefficients to graph

y = | x - 1| .

2-2

2nd F SUB

ENTER

8-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

N o te s

*Use either pen touch or cursor to operate.

2-3

2-4

View the graph.

Notice that placing an h (>0)

within the standard form

y = a| x - h| + k will move the

graph right h units on the x-

axis.

GRAPH

Change the coefficients to graph

y =| x| -1.

2nd F

SUB

ENTER

( )

ENTER

Notice that adding a k (>0)

within the standard form

y=a| x-h| +k will move the

graph up k units on the y-axis.

View the graph.

2-5

GRAPH

The EL-9650/9600c shows absolute values with | | , just as written on paper, by using the

Equation editor. Use of the calculator allows various absolute value functions to be

graphed quickly and shows their characteristics in an easy-to-understand manner.

8-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Shifting a graph of Absolute Value Functions

The absolute value of a real number x is defined by the following:

| x| =

x if x ≥ 0

-x if x ≤ 0

If n is a positive number, there are two solutions to the equation | f (x)| = n because there

are exactly two numbers with the absolute value equal to n: n and -n. The existence of two

distinct solutions is clear when the equation is solved graphically.

An absolute value function can be presented as y = a| x - h| + k. The graph moves as the

changes of slope a, x-intercept h, and y-intercept k.

Ex a m p le

Move and change graphs of absolute value function y =| x| to check the relation

between the graphs and the values of coefficients.

1. Move the graph y = | x| downward by 2 using the Shift feature.

2. Move the graph y = | x| to the right by 2 using the Shift feature.

3. Pinch the slope of y = | x| to 2 or minus using the Change feature.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

1-1 Access the Shift feature.

Select y = | x| .

2nd F SHIFT/CHANGE

(

)

ENTER

ALPHA

Move the graph downward by 2.

1-2

1-3

y =| x| changes to y = | x| -2

ENTER

Save the new graph and look at the

relationship of the function and the

graph.

The graph of the equation that

is highlighted is shown by a

solid line. Notice that the y-

intercept k in the standard

form y = a | x - h| + k takes

charge of vertical movement

of the graph.

ENTER

ALPHA

8-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

-1

Move the original graph to the right

by 2.

y = | x| changes to y = | x-2|

ALPHA

ENTER

2-2

Save the new graph and look at the

relationship of the function and the

graph.

Notice that the function h in

the standard form

y = a| x - h| + k takes charge

of horizontal movement of

the graph.

ENTER ALPHA

Access the Change feature.

2nd F SHIFT/CHANGE

Select y = | x| .

Make the slope of the graph steeper.

Save the new graph.

y = | x| © y = 2| x|

ENTER

Make the slope of the graph minus.

Save the new graph.

y = | x| © y = - | x|

ENTER

Notice that the coefficient a

in the standard form

y = a | x - h| + k takes

charge of changing the slope.

Look at the relationship of the

function and the graph.

ALPHA

EL-9650/9600c/9450/9400 shows absolute values with | | , just as written on paper, by

using the Equation editor. Use of the calculator allows various absolute value functions

to be graphed quickly and shows their characteristics in an easy-to-understand manner.

The Shift/Change feature of the EL-9650/9600c/9450/9400 allows visual understanding

of how graph changes affect the form of absolute value functions.

8-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Solving Absolute Value Equations

The absolute value of a real number x is defined by the following:

| x| =

x if x ≥ 0

-x if x ≤ 0

If n is a positive number, there are two solutions to the equation | f (x)| = n because there

are exactly two numbers with the absolute value equal to n: n and -n. The existence of two

distinct solutions is clear when the equation is solved graphically.

Ex a m p le

Solve an absolute value equation | 5 - 4x| = 6

There may be differences in the results of calculations and graph plotting depending on the setting.

Sta r tin g Return all settings to the default value and delete all data.

Be fo re

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Enter y = | 5 - 4x| for Y1.

Enter y = 6 for Y2.

—

MATH

X/ /T/n

ENTER

There are two points of in-

tersection of the absolute

value graph and the hori-

zontal line y = 6.

View the graph.

GRAPH

The solution to the equation

| 5 - 4x| = 6 consists of the two

values -0.25 and 2.75. Note

that although it is not as intu-

itively obvious, the solution

could also be obtained by

finding the x-intercepts of the

function y = | 5x - 4| - 6.

Find the points of intersection of

the two graphs and solve.

2nd F CALC

The EL-9650/9600c/9450/9400 shows absolute values with | | , just as written

on paper, by using the Equation editor. The graphing feature of the calculator

shows the solution of the absolute value function visually.

8-3

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Solving Absolute Value Inequalities

To solve an inequality means to find all values that make the inequality true. Absolute value

inequalities are of the form | f (x)| < k,

f (x)| ≤ k,

f (x)| > k, or

f (x)

≥

k. The graphical

solution to an absolute value inequality is found using the same methods as for normal

inequalities. The first method involves rewriting the inequality so that the right-hand side of

the inequality is 0 and the left-hand side is a function of x. The second method involves

graphing each side of the inequality as an individual function.

Ex a m p le

Solve absolute value inequalities in two methods.

1. Solve 20 -

< 8 by rewriting the inequality so that the right-hand side of

the inequality is zero.

2. Solve 3.5x + 4 > 10 by shading the solution region.

There may be differences in the results of calculations and graph plotting depending on the setting.

Sta r tin g Return all settings to the default value and delete all data.

Be fo re

Set viewing window to “-5< x <50,” and “-10< y <10” using Rapid Window feature to solve Q1.

WINDOW

ENTER

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

1-1

1-2

Rewrite the equation.

| 20 -

| < 8

©| 20 -

| - 8 < 0.

Enter y = | 20 -

| - 8 for Y1.

MATH

—

X/ /T/

—

1-3

1-4

The intersections with the x-

axis are (10, 0) and (23.3, 0)

( Note: The value of y in the

x-intercepts may not appear

exactly as 0 as shown in the

example, due to an error

caused by approximate calcu-

lation.)

View the graph, and find the

x-intercepts.

GRAPH

2nd F CALC

y = 0.00000006 ( Note)

Solve the inequality.

Since the graph is below the

x-axis for x in between the

two x-intercepts, the solution

is 10 < x < 23.3.

8-4

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Enter the function

y =| 3.5x + 4| for Y1.

Enter y = 10 for Y2.

2-1

MATH

•

X/ /T/n

ENTER

Since the inequality you are

solving is Y1 > Y2, the solu-

tion is where the graph of Y2

is “on the bottom” and Y1 in

“on the top.”

2-2

2-3

Set up shading.

2nd F DRAW

—

Set viewing window to “-10 < x <

10” and “-5 < y < 50” using Rapid

Window feature and view the graph.

WINDOW

ENTER

The intersections are (-4, 10)

and (1.7, 10.0). The solution

is all values of x such that

x <-4 or x >1.7.

( Note: The value of y in the

intersection of the two graphs

may not appear exactly as 10

as shown in the example, due

to an error caused by approxi-

mate calculation.)

Find the points of intersection.

Solve the inequality.

-4

2nd F CALC

y = 9.999999999 ( Note)

The EL-9650/9600c/9450/9400 shows absolute values with | | , just as written

on paper, by using the Equation editor. Graphical solution methods not only

offer instructive visualization of the solution process, but they can be applied to

inequalities that are often difficult to solve algebraically. The Shade feature is

useful to solve the inequality visually and the points of intersection can be

obtained easily.

8-4

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Evaluating Absolute Value Functions

The absolute value of a real number x is defined by the following:

| x| =

x if x ≥ 0

-x if x ≤ 0

Note that the effect of taking the absolute value of a number is to strip away the minus sign

if the number is negative and to leave the number unchanged if it is nonnegative.

Thus, | x| ≥ 0 for all values of x.

Ex a m p le

Evaluate various absolute value functions.

1. Evaluate | - 2(5-1)|

2. Is | -2+7| = | -2| + | 7| ?

Evaluate each side of the equation to check your answer.

Is | x + y| =| x| + | y| for all real numbers x and y ?

If not, when will | x + y| = | x| +| y| ?

6-9

1+3

| 6-9|

| 1+3|

3. Is |

| =

Evaluate each side of the equation to check your answer. Investigate with

more examples, and decide if you think | x / y| =| x| /| y|

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Access the home or computation

screen.

1-1

1-2

The solution is 8.

Enter y = | -2(5-1)| and evaluate.

( )

—

MATH

(

)

ENTER

2-1

| -2 + 7| = 5, | -2| + | 7| = 9

Evaluate| -2 + 7| . Evaluate| -2| +| 7| .

( )

MATH

ENTER

MATH

( )

ENTER

8-5

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Is | x + y| = | x| +| y| ? Think about

this problem according to the cases

when x or y are positive or negative.

2-2

If x ≥ 0 and y ≥ 0

[e.g.; (x, y) = (2,7)]

| x +y| = | 2 + 7| = 9

| x| +| y| = | 2| + | 7| = 9

If x ≤ 0 and y ≥ 0

[e.g.; (x, y) = (-2, 7)]

| x +y| = | -2 + 7| = 5

| x| +| y| = | -2| + | 7| = 9

If x ≥ 0 and y ≤ 0

[e.g.; (x, y) = (2, -7)]

| x +y| = | 2-7| = 5

| x| +| y| = | 2| + | -7| = 9

If x ≤ 0 and y ≤ 0

[e.g.; (x, y) = (-2, -7)]

| x +y| = | -2-7| = 9

| x| +| y| = | -2| + | -7| = 9

Therefore | x +y| =| x| +| y| when x ≥ 0 and y ≥ 0,

and when x ≤ 0 and y ≤ 0.

6-9

1+3

6-9

1+3

6-9

1+3

6-9

1+3

Evaluate

. Evaluate

3-1

3-2

= 0.75 ,

= 0 .75

6-9

1+3

6-9

1+3

MATH

—

ENTER

—

MATH

ENTER

Is | x /y| = | x| /| y| ?

Think about this problem according

to the cases when x or y are positive

or negative.

If x ≥ 0 and y ≥ 0

[e.g.; (x, y) = (2,7)]

| x /y| = | 2/7| = 2/7

| x| /| y| = | 2| /| 7| = 2/7

If x ≤ 0 and y ≥ 0

[e.g.; (x, y) = (-2, 7)]

| x /y| = | (-2)/7| = 2/7

| x| /| y| = | -2| /| 7| = 2/7

If x ≥ 0 and y ≤ 0

[e.g.; (x, y) = (2, -7)]

| x /y| = | 2/(-7)| = 2/7

| x| /| y| = | 2| /| -7| = 2/7

If x ≤ 0 and y ≤ 0

[e.g.; (x, y) = (-2, -7)]

| x /y| = | (-2)/-7| = 2/7

| x| /| y| = | -2| /| -7| = 2/7

The statement is true for all y ≠ 0.

The EL-9650/9600c/9450/9400 shows absolute values with | | , just as written

on paper, by using the Equation editor. The nature of arithmetic of the absolute

value can be learned through arithmetical operations of absolute value functions.

8-5

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Graphing Rational Functions

p (x)

q (x)

A rational function f (x) is defined as the quotient

where p (x) and q (x) are two

polynomial functions such that q (x) ≠ 0. The domain of any rational function consists of all

values of x such that the denominator q (x) is not zero.

A rational function consists of branches separated by vertical asymptotes, and the values of

x that make the denominator q (x) = 0 but do not make the numerator p (x) = 0 are where

the vertical asymptotes occur. It also has horizontal asymptotes, lines of the form y = k (k,

a constant) such that the function gets arbitrarily close to, but does not cross, the horizontal

asymptote when | x| is large.

The x intercepts of a rational function f (x), if there are any, occur at the x-values that make

the numerator p (x), but not the denominator q (x), zero. The y-intercept occurs at f (0).

Ex a m p le

Graph the rational function and check several points as indicated below.

x-1

Graph f (x) =

x²-1

Find the domain of f (x), and the vertical asymptote of f (x).

3. Find the x- and y-intercepts of f (x).

4. Estimate the horizontal asymptote of f (x).

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Set the zoom to the decimal window:

(

)

ZOOM

ENTER

ALPHA

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

x - 1

Enter y =

for Y1.

1-1

1-2

x²-1

x ²

—

X/ /T/n

View the graph.

The function consists of two

branches separated by the verti-

cal asymptote.

GRAPH

9-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Find the domain and the vertical

asymptote of f (x), tracing the

graph to find the hole at x = 1.

Since f (x) can be written as

x - 1

, the domain

(x + 1)(x - 1)

consists of all real numbers x

such that x ≠ 1 and x ≠ -1.

There is no vertical asymptote

where x = 1 since this value

of x also makes the numera-

tor zero. Next to the coordi-

nates x = 0.9, y = 0.52, see that

the calculator does not display

a value for y at x = 1 since 1

is not in the domain of this

rational function.

(repeatedly)

TRACE

The y-intercept is at (0 ,1). No-

tice that there are no x-inter-

cepts for the graph of f (x).

Find the x- and y-intercepts of f (x).

2nd F CALC

The line y = 0 is very likely a

horizontal asymptote of f (x).

Estimate the horizontal asymptote

of f (x).

The graphing feature of the EL-9650/9600c/9450/9400 can create the branches

of a rational function separated by vertical asymptote. The calculator allows

the points of intersection to be obtained easily.

9-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Solving Rational Function Inequalities

p (x)

q (x)

A rational function f (x) is defined as the quotient

where p (x) and q (x) are two

polynomial functions such that q (x) ≠ 0. The solutions to a rational function inequality can

be obtained graphically using the same method as for normal inequalities. You can find the

solutions by graphing each side of the inequalities as an individual function.

Ex a m p le

Solve a rational inequality.

Solve

≤ 2 by graphing each side of the inequality as an individual function.

1 - x²

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Set the zoom to the decimal window:

(

)

ZOOM

ENTER

ALPHA

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Enter y =

for Y2.

for Y1. Enter y = 2

1- x²

MATH

X/ /T/n

x ²

—

X/ /T/n

ENTER

Since Y1 is the value “on the

bottom” (the smaller of the

two) and Y2 is the function

“on the top” (the larger of the

two), Y1 < Y < Y2.

Set up the shading.

2nd F

DRAW

—

View the graph.

GRAPH

The intersections are when

x = -1.3, -0.8, 0.8, and 1.3.

The solution is all values of

x such that x ≤ -1.3 or

Find the intersections, and solve the

inequality.

Do this four times

2nd F CALC

-0.8 ≤ x ≤ 0.8 or x ≥ 1.3.

The EL-9650/9600c/9450/9400 allows the solution region of inequalities to be

indicated visually using the Shade feature. Also, the points of intersections

can be obtained easily.

9-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Graphing Parabolas

The graphs of quadratic equations (y = ax ²+ bx + c) are called parabolas. Sometimes the quadratic

equation takes on the form of x = ay²+ by + c.

There is a problem entering this equation in the calculator graphing list for two reasons:

a) it is not a function, and only functions can be entered in the Y= list locations,

b) the functions entered in the Y= list must be in terms of x, not y.

There are, however, two methods you can use to draw the graph of a parabola.

Method 1: Consider the "top" and "bottom" halves of the parabola as two different parts of the graph

because each individually is a function. Solve the equation of the parabola for y and enter the two parts

(that individually are functions) in two locations of the Y= list.

Method 2: Choose the parametric graphing mode of the calculator and enter the parametric equations

of the parabola. It is not necessary to algebraically solve the equation for y. Parametric representations

are equation pairs x = F(t), y = F(t) that have x and y each expressed in terms of a third parameter, t.

Ex a m p le

Graph a parabola using two methods.

1. Graph the parabola x = y²-2 in rectangular mode.

2. Graph the parabola x = y²-2 in parametric mode.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Set the zoom to the decimal window:

(

)

ZOOM

ENTER

ALPHA

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

x = y²-2

x + 2 = y²

Solve the equation for y.

1-1

1-2

√

y =

x + 2

–

Enter y =

√x+2 for Y1 and enter

y = -Y1 for Y2.

2nd F

√

( )

ENTER

VARS

ENTER

The graph of the equation y =

x+ 2 is the "top half" of the

parabola and the graph of the

equation y = - x + 2 gives

the "bottom half."

1-3

View the graph.

√

GRAPH

√

10-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

Change to parametric mode.

2-1

2-2

2nd F SET UP

Rewrite x = y²-2 in parametric form.

Let y = T and substitute in x

Enter X1T = T ²-2 and Y1T = T.

= y²- 2, to obtain x = T²- 2.

x ²

—

X/ /T/n

ENTER

X/ /T/n

The graph starts at T =0 and

increases. Since the window

setting is T ≥ 0, the region T

< 0 is not drawn in the graph.

View the graph. Consider why only

half of the parabola is drawn.

(To understand this, use Trace fea-

ture.)

2-3

GRAPH

TRACE

(

)

Set Tmin to -6.

2-4

2-5

WINDOW

( )

ENTER

View the complete parabola.

GRAPH

The calculator provides two methods for graphing parabolas, both of which

are easy to perform.

10-1

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Graphing Circles

The standard equation of a circle of radius r that is centered at a point (h, k) is (x - h) ²+

(y - k) ²= r ². In order to put an equation in standard form so that you can graph in

rectangular mode, it is necessary to solve the equation for y. You therefore need to use the

process of completing the square.

Ex a m p le

Graph the circles in rectangular mode. Solve the equation for y to put it in the

standard form.

1. Graph x ²+ y²= 4.

2. Graph x ²- 2x + y²+ 4y = 2.

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Set the zoom to the decimal window:

(

)

ZOOM

ENTER

ALPHA

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

y²= 4 - x²

Solve the equation for y.

1-1

√

Enter y = 4 - x for Y1 (the top

y = √4 - x

–

√

half). Enter y = - 4 - x for Y2.

x ²

X/ /T/n

2nd F

—

√

( )

ENTER

VARS

ENTER

This is a circle of radius r ,

centered at the origin.

1-2

2-1

View the graph.

GRAPH

x²- 2x + y²+ 4y = 2

Place all variable terms on the

left and the constant term on

the right-hand side of the

equation.

Solve the equation for y,

completing the square.

x²-2x+y²+4y+4=2+4 Complete the square on the

y-term.

x²- 2x + (y+2)²= 6

Express the terms in y as a

perfect square.

(y+2)²= 6 -x²+ 2x

Leave only the term involving

y on the left hand side.

√

y+2 = ± 6-x +2x

Take the square root of both

sides.

√

y = ± 6-x +2x -2

Solve for y.

10-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

√

Notice that if you enter

y = 6 - x + 2x - 2 for Y1

and y = - Y1 for Y2, you will

not get the graph of a circle

because the “±” does not go

with the “-2”.

Enter y = 6 - x + 2x for Y1,

2-2

√

y = Y1 - 2 for Y2, and y = -Y1 -2 for

Y3.

—

x²

2nd F

X/ /T/n

√

X/ /T/

ENTER

—

VARS

ENTER

VARS

ENTER

( )

—

"Turn off" Y1 so that it will not

graph.

2-3

Notice that “=” for Y1 is no

longer darkened. You now

have the top portion and the

bottom portion of the circle

in Y2 and Y3.

ENTER

2-4

2-5

View the graph.

GRAPH

Adjust the screen to see the bottom

part of the circle using the Rapid

feature.

Wait until the graph is dis-

played after each operation.

(It takes few seconds to

graph)

ENTER

2-6

View the graph in the new window.

GRAPH

Graphing circles can be performed easily on the calculator display. Also,

the Rapid Zoom feature of the EL-9650/9600c/9450/9400 allows shifting and

adjusting display area (window) of a graph easily.

10-2

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Graphing Ellipses

The standard equation for an ellipse whose center is at the point (h, k) with major and

(x - h) ²

(y - k) ²

= 1.

minor axes of length a and b is

a ²

b ²

There is a problem entering this equation in the calculator graphing list for two reasons:

a) it is not a function, and only functions can be entered in the Y = list locations.

b) the functions entered in the Y = list locations must be in terms of x, not y.

To draw a graph of an ellipse, consider the “top” and “bottom” halves of the ellipse as two

different parts of the graph because each individual is a function. Solve the equation of the

ellipse for y and enter the two parts in two locations of the Y = list.

Ex a m p le

Graph an ellipse in rectangular mode. Solve the equation for y to put it in the

standard form.

Graph the ellipse 3(x -3) ²+ (y + 2) ²= 3

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Set the zoom to the decimal window:

(

)

ZOOM

ENTER

ALPHA

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

3(x - 3)²+ (y + 2)²= 3

(y + 2)²= 3 - 3(x - 3)²

3 - 3(x - 3)²

Solve the equation for y, completing

the square.

Enter

y + 2 =

√

Y1 = 3 - 3(x - 3)

y =

√

3 - 3(x - 3)²- 2

Y2 = Y1 - 2

Y3 = -Y1 -2

2nd F

—

(

)

√

x²

—

ENTER

X/ /T/

—

VARS

ENTER

( )

VARS

ENTER

—

Turn off Y1 so that it will not graph.

ENTER

10-3

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

View the graph.

GRAPH

Adjust the screen to see the bottom

part of the ellipse using the Rapid

Zoom feature.

Wait until the graph is dis-

played after each operation.

(It takes few seconds to

graph)

ENTER

View the graph in the new window.

GRAPH

Graphing an ellipse can be performed easily on the calculator display. In

addition to the Zoom-in/Zoom-out features, the EL-9650/9600c/9450/9400 have

the Rapid Zoom feature to adjust the display easily.

10-3

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Graphing Hyperbolas

The standard equation for a hyperbola can take one of two forms:

( y - k )²

( x - h )²

= 1 with vertices at ( h ± a, k ) or

a²

b²

( y - h)²

( x - k )²

b²

= 1 with vertices at ( h, k ± b ).

a²

There is a problem entering this equation in the calculator graphing list for two reasons:

a) it is not a function, and only functions can be entered in the Y= list locations.

b) the functions entered in the Y= list locations must be in terms of x, not y.

To draw a graph of a hyperbola, consider the “top” and “bottom” halves of the hyperbola

as two different parts of the graph because each individual is a function. Solve the equation

of the hyperbola for y and enter the two parts in two locations of the Y= list.

Ex a m p le

Graph a hyperbola in rectangular mode. Solve the equation for y to put it in the

standard form.

Graph the hyperbola x²+ 2x - y²- 6y + 3 = 0

There may be differences in the results of calculations and graph plotting depending on the setting.

Return all settings to the default value and delete all data.

Be fo re

Sta r tin g

Set the zoom to the decimal window:

(

)

ZOOM

ENTER

ALPHA

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

x²+ 2x - y²-6y = -3

x²+ 2x - (y²+ 6y + 9) = -3 -9

x²+ 2x - (y +3)²= -12

Solve the equation for y completing

the square.

Enter

Y1 =

Y2 = Y1 -3

Y3 = -Y1 -3

√

x²+ 2x + 12

(y + 3)²= x²+ 2x + 12

y + 3 =

√

x²+ 2x + 12

x²+ 2x + 12 - 3

y =

√

x²

X/ /T/

2nd F

√

/θ/T/n

ENTER

VARS

ENTER

—

ENTER

( )

—

VARS

ENTER

Turn off Y1 so that it will not graph.

ENTER

10-4

Download from Www.Somanuals.com. All Manuals Search And Download.

EL-9650/9600c/9450/9400 Graphing Calculator

Ste p & Ke y O p e ra tio n

Disp la y

(When using EL-9650/9600c)

N o te s

(When using EL-9650/9600c)

*Use either pen touch or cursor to operate.

View the graph.

GRAPH

Zoom out the screen.

ZOOM

Graphing hyperbolas can be performed easily on the calculator display. In

addition to the Zoom-in/Zoom-out features, the EL-9650/9600c/9450/9400 have

the Rapid Zoom feature to adjust the display easily. (See the section “Graphing

Ellipses (No. 10-3)” about how to use the Rapid Zoom feature.)

10-4

Download from Www.Somanuals.com. All Manuals Search And Download.

Key pad for the SHARP EL-9650/9600c Calculator

Cursor movement keys

Graphing keys

Clear/Quit key

Power supply ON/OFF key

Alphabet specification key

Secondary function specification key

Display screen

Variable enter key

Calculation execute key

Communication port for peripheral devices

Download from Www.Somanuals.com. All Manuals Search And Download.

Key pad for the SHARP EL-9450/9400 Calculator

Cursor movement keys

Graphing keys

Clear/Quit key

Power supply ON/OFF key

Alphabet specification key

Secondary function specification key

Display screen

Variable enter key

Calculation execute key

Communication port for peripheral devices

Download from Www.Somanuals.com. All Manuals Search And Download.

Use this form to send us your contribution

Dear Sir/Madam

We would like to take this opportunity to invite you to create a mathematical problem which can be solved

with the SHARP graphing calculator EL-9650/9600c/9450/9400. For this purpose, we would be grateful if

you would complete the form below and return it to us by fax or mail, specifying which calculator you are

writing problems for, the EL-9650/9600c or 9450/9400.

If your contribution is chosen, your name will be included in the next edition of The EL-9650/9600c/9450/

9400 Graphing Calculator Handbook. We regret that we are unable to return contributions.

We thank you for your cooperation in this project.

(

)

Name:

Mr.

Ms.

School/College/Univ.:

Address:

Post Code:

Country:

Phone:

E-mail:

Fax:

* You are making this sheet for the (

EL-9650/9600c,

EL-9450/9400).

SUBJECT : Write a title or the subject you are writing about.

INTRODUCTION : Write an explanation about the subject.

EXAMPLE : Write example problems.

SHARP Graphing Calculator

Download from Www.Somanuals.com. All Manuals Search And Download.

BEFORE STARTING : Write any conditions to be set up before solving the problems.

STEP

NOTES

SHARP CORPORATION Osaka, Japan

Fax:

SHARP Graphing Calculator

Download from Www.Somanuals.com. All Manuals Search And Download.

SH ARP CORPORATION OSAKA, JAPAN

Download from Www.Somanuals.com. All Manuals Search And Download.

Shark Vacuum Cleaner UV611TR User Manual
Sony Flat Panel Television VGCLA38G User Manual
Sony Flat Panel Television VPCL21SFX W User Manual
Sony Security Camera NTSC PAL User Manual
Sony Speaker System Model CMT CP1 User Manual
Stamina Products Home Gym 55 5510 User Manual
Suunto Scuba Diving Equipment SS021646000 User Manual
Swisher Lawn Mower RTB1254412V POLB10544HD RTB105441 User Manual
Sybase Server DC38029 01 0500 01 User Manual
Sylvania Flat Panel Television 6626LG User Manual