Sharp EL9900 manual Using this Handbook, Introduction

Using this Handbook

This handbook was produced for practical application of the SHARP EL-9900 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.

Introduction

Notes

EL-9900 Graphing Calculator

Slope and Intercept of Quadratic Equations

Explains the process of each

Explanation of the section

step in the key operations

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 = ax2 + 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

Example

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

Example

coefficients a, h, and k.

Example of a problem to be

EL-9900 Graphing Calculator

Graph various quadratic equations and check

the relation between the graphs and

the values of coefficients of the equations.

solved in the section

1. Graph y = x 2

and y = (x-2)2.

Step & Key Operation

Display

Notes

*Use either pen touch or cursor to operate.

Graph y = x

and y = x +2.

2

2.

2

2

2-1

3. Graph y = x 2

and y = 2x 2.

Change the equation in Y2 to y = x +2.

4. Graph y = x 2

and y = -2x 2.

Y=

0

*

2nd F

SUB

ENTER

2

ENTER

Before

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

Before Starting

Starting

Return all settings to the default value and delete2all-2dataView.

both graphs.

Notice that the addition of 2 moves

basic graph down two units on

the basic y =x2 graph up two units

GRAPH

and the addition of -2 moves the

Important notes to read

Step & Key Operation

Display

Notes

the y-axis. This demonstrates the

h)2

+ k will move the basic graph up k units and placing k

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

before operating the calculator

1-1Enter the equation y = x2 for Y1.

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

Y=

X/θ /T/n

x2

axis.

the equation in Y2 to y = 2x2.

1-2

3-1Change

Enter the equation y = (x-2) 2

for

Y=

2

ENTER

*

2nd F

SUB

Y2 using Sub feature.

0 ENTER

Step & Key Operation

( X/θ /T/n —

ALPHA

A

3-2

2 pinches2

or closes the basic

x2

+

View both graphs.

Notice that the multiplication of

ALPHA

H

)

ALPHA

K

A clear step-by-step guide

1 ENTER

2 ENTER

GRAPH

y=x graph. This demonstrates

2nd F

SUB

( 0

ENTER

)

(x - h)2 + k will pinch or close

the fact that multiplying an a

to solving the problems

1-3

(> 1) in the standard form y = a

View both graphs.

within the quadratic operation

the basic graph.

Notice that the addition of -2

GRAPH

4-1

moves the basic

y =x2 graph

Change rightthe equationtwo unitsin(addingY2 to 2 moves

y = -2x2.it left two units) on the x-axis.

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

form y = a (x - hY=)2 + k will

move2nd F

theSUB

basic(-)graph2 right

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

Display

on the x-axis. ENTER

4-2

GRAPH

4-1

y =x2 graph and flips it (reflects

View both graphs.

Notice that the multiplication of

Illustrations of the calculator

-2 pinches or closes the basic

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

it) across the x-axis. This dem-

screen for each step

onstrates the fact that multiply-

will pinch or

close the basic graph and flip it (reflect

it) across the x-axis.

The EL-9900 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,

Merits of Using the EL-9900

using the Substitution feature.

4-1

Highlights the main functions of the calculator relevant to the section

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.)