USING THE

TI- 83 GRAPHICS CALCULATOR

By Philip Romano

01/01

CONTENTS

To the student 3

Some Common Keys 4

Basic Computations 6

Setting the Viewing Window 9

Graphing a Function 10

Finding the Intersection of 2 Curves 11

Finding the Relative Max/Min 13

Finding the x-intercepts of a Function 14

Graphing a Piecewise Function 15

Creating a Table of Values 17

Entering a Matrix for Calculations 19

Evaluating the Determinant of a Matrix 21

Solving Inequalities Graphically 22

Evaluating Radicals 25

Quadratic Formula Program 29

TO THE STUDENT:

As you prepare to learn a particular skill in this booklet, you should first read through the

entire discussion of that skill to get an overview of the procedure being described. Then, with

calculator in hand, actually go through the keystrokes on your calculator. As you press a

key, look up at the screen to see the effect of each such keystroke. You will find that the

actual working through of the procedure on your calculator, rather than just reading the

procedure, will be an immense help.

SOME COMMON KEYS TI-83

You should locate each of these keys on your calculator. You will learn their use as

you work through the examples that follow.

( - ) negative sign key, used to make a number or

quantity negative

2nd accesses the function or object written above a key

Alpha accesses letters of the alphabet

Clear clears a line or the screen

Window takes you to the screen to establish viewing window

Math accesses math menu for math computations

Mode accesses the modes of the calculator

1

2nd 0 ENTER accesses the absolute value

Notes:

1. The cursor keys are the directional arrow keys located at the top right corner

of the keypad right below the Trace and Graph keys. They are used to move the

cursor around on the screen ; they have other uses also.

2. Press the keys 2nd Mode to quit and return to the home screen.

3. Press and release 2nd , then press and hold down the up cursor key

to darken screen.

4. Press and release 2nd , then press and hold down the down cursor key

to lighten screen.

4. Press 2nd ON to turn the calculator off.

2

BASIC COMPUTATIONS TI-83

You need parentheses around the numerator and denominator, but you do not

need parentheses around the 3/7 in the denominator since the division of 3 by

7 will be done before the subtraction. Also, note the negative sign key (-) used

for the negative sign before the 3 in the denominator as opposed to the subtraction

key used for the subtraction in the denominator.

ENTER

The answer is - 11.08516403

7

The answer is 3.448798951

7

The answer is .8773703791

Note that the parentheses are needed around the numerator.

The answer is 3.65930571 The parentheses are needed around the exponent.

3

5. Scientific Notation

To enter a number in scientific notation, you will use the EE option which is

located above the comma key , . To access the EE option, you first press

the 2nd key and then the comma key.

Press 5 . 3 4 2nd , (-) 2 3

The display will appear as 5.34E-23

6. Accessing the previous answer

If you perform a calculation and then wish to use that answer in the next calculation,

you can access the previous answer by pressing 2nd (-) .

For example , divide 3 by 7 and press enter to evaluate. The answer is .4285714286

Now if you wish to raise 4 to that number, press

4 ^ 2nd (-) The display will appear as 4^Ans. Press ENTER

to get an answer of 1.811447329

7. Changing a decimal answer to a fraction

To change a decimal to a fraction, use the 1st option under the MATH menu.

4

Now press MATH 1 ENTER to get an answer of 22/15

answer is converted to a fraction.

5

VIEWING WINDOW TI-83

The viewing window for a graph is the portion of the coordinate system shown

on the screen.

Xmin: leftmost value on x-axis

Xmax: rightmost value on x-axis

Xscl: number of units between each tick mark on x-axis

Ymin: lowermost value on y-axis

Ymax: uppermost value on y-axis

Yscl: number of units between each tick mark on the y-axis

Ymax

Xmin Xmax

Ymin

Notation is Xmin, Xmax by Ymin, Ymax . For example, set the viewing window

is

30, Ymin is -25 , Ymax is 15, and the number of units between each tick mark on the x

and

y axis is 5 units.

Press Window

Press -40 and Enter , 30 and Enter , 5 Enter , and so on.

You can quickly set this window by pressing Zoom 6 .

3

GRAPHING A FUNCTION TI-83

Example:

3. Establish a viewing window as explained before by pressing WINDOW

and entering appropriate values.

4. Press GRAPH

OR

the function in the standard window, if that is a good window. You do not

need to press GRAPH in this case.

4

FINDING THE INTERSECTION OF 2 CURVES TI-83

To find the intersection of 2 curves, you enter the expressions for both functions

Example:

3. Graph the lines in an appropriate viewing window; the intersection point must

appear in the window, so you may need to experiment with different window

settings.

4. Press 2nd TRACE to access the ”CALCULATE” menu. Press 5 for

INTERSECT.

5. The calculator will ask for ”FIRST CURVE?” . The cursor should be on the first

curve as indicated by the function shown in the upper left of the screen. You confirm

that the cursor is on the first curve by pressing ENTER .

6. The calculator will then ask for ”SECOND CURVE?” . You answer by pressing

ENTER .

7. The calculator will ask for a ”GUESS?” . You should move the cursor near the point

of intersection using the left and right cursor keys. Once the cursor is near the point,

press ENTER .

The x and y coordinates of the intersection point will appear at the bottom of the

screen.

Note: For some problems, just the x-coordinate is the answer and, for other problerms,

5

both coordinates are required.

6

FINDING THE MAXIMUM AND MINIMUM ( RELATIVE MAX/MIN ) TI - 83

To find the maximum or minimum of a function f(x) , first graph f(x) in an

appropriate viewing window. The maximum or minimum point should appear

in the window.

Press 2nd TRACE to access the CALCULATE menu. Choose 3 for

minimum and 4 for maximum.

Example :

3. Press GRAPH to graph the function.

4. Press 2nd TRACE and choose option 3 for minimum.

5. The calculator asks for ”LEFT BOUND?” . Move the cursor to a point to the left

of the minimum point and press ENTER . You use the left and right cursor keys

to move the cusor left and right.

6. The calculator asks for ”RIGHT BOUND?” . Move the cursor to the right of the

minimum point and press ENTER .

7. The calculator asks for ”GUESS?” . Move the cursor near the minimum point , but

make sure your cursor is between the 2 bounds you set above. Press ENTER .

The x and y coordinates of the minimum point appear at the bottom of the screen, in

6

FINDING THE X - INTERCEPTS OF A FUNCTION TI-83

To find the x - intercept of a function f(x) , first graph f(x) in an appropriate

viewing window so that the x - intercept appears in the window.

Press 2nd TRACE to access the CALCULATE menu. Choose option 2 ”ZERO” ,

which is another name for x - intercept. Some calculators may use the term ”ROOT” .

Example :

5,

3. Press GRAPH to graph the function.

4. Press 2nd TRACE and choose option 2.

5. The calculator asks for ”LEFT BOUND?” . Move the cursor ( using the left or right

cursor

keys) to the left of the x - intercept and press ENTER .

6. The calculator asks for ”RIGHT BOUND?” . Move the cursor to the right of the x

-intercept

and press ENTER .

7. The calculator asks for ”GUESS?” . Move the cursor near the x - intercept , but

make

sure the cursor is between the 2 bounds you set above. Press ENTER .

The word ”ZERO” will appear at the bottom of the screen and the x - coordinate shown

is the x - intercept. For this example, the x - intercept is - 1.476 , rounded to 3 places.

7

GRAPHING PIECEWISE-DEFINED FUNCTIONS TI-83

To graph a piecewise function, you enter the first piece (in parentheses) juxtaposed

parentheses)

pieces.

Note: 1. To access the inequality symbols , press 2nd MATH to go to the TEST

menu.

2. If there are breaks in the graph, it may be best to graph in DOT mode rather

than CONNECTED mode. Press MODE and move the cursor down to

”Connected” and over to ”Dot” and press ENTER .

should

5)

Example :

8

in DOT mode.

and

sure

to graph in DOT mode.

9

CREATING A TABLE OF VALUES TI - 83

General Remarks

access the TABLE SETUP menu, press 2nd WINDOW .

”TblStart” defines the first x value to appear in the table; you can begin with any x

value.

change

in the x column; you can set this increment to be any value.

”Indpnt” represents the x variable and ”Depend” represents the y variable. Setting both

of these to ”Auto” will allow the table to be automatically generated. If you set ”Indpnt”

to

”Ask” , you can input any x value when you go to the table.

Example:

2. Press 2nd WINDOW (-) 3 ENTER .

3. Press 1 ENTER to set the increment of the x values to 1.

4. Set both ”Indpnt” and ”Depend” to ”Auto” . You may need to move the cursor

down and press ENTER for the ”Depend” option.

5. Press 2nd GRAPH to create the table.

Notes : 1. Move the cursor up or down to find more values of x as the table extends

indefinitely in both directions.

2. Move the cursor right to the y column and the corresponding y value is

displayed in its entirety at the bottom of the screen.

3. You can make a table of values for as many as ten functions. For example,

if

10

you enter five functions and create a table of values as above, move the

cursor

to the right to display the other functions once you go to the actual table.

11

ENTERING A MATRIX FOR CALCULATIONS TI-83

To access the MATRIX menu , press MATRIX . There are 3 sub-menus to

choose;

NAMES menu accesses the names of the matrices; to perform calculations with a

matrix , you must call up the name of the matrix.

MATH menu accesses various matrix mathematical functions for computations.

EDIT menu allows you to enter a new matrix or change an already existing

matrix.

Example:

Enter the matrix

1 0 4

into the matrix A .

1. Press MATRIX and move the cursor over to EDIT , press ENTER to access

the

matrix A. You would choose the number of the matrix if you want another matrix,

such

as 2 formatrixB, 3 for matrix C , and so on.

2. Press 3 ENTER 3 ENTER to enter the size of the matrix. The first number

is

the number of rows and the second number is the number of columns.

3. Press 2 ENTER (-) 1 ENTER 5 ENTER 3 ENTER 6

ENTER

(-) 2 ENTER 1 ENTER 0 ENTER 4 ENTER to enter the

entries

11

of the matrix.

4. Press 2nd MODE to return to the Home screen.

12

EVALUATING THE DETERMINANT OF A MATRIX TI - 83

1. Enter the matrix into the name A as described previously. You can enter the matrix

under any name you wish.

2. Return to the Home screen after you enter the matrix by pressing 2nd MODE .

3. Press MATRIX and move cursor over to the MATH menu and press ENTER

to choose option 1 for ” det( ” , which represents the determinant function.

4. Press MATRIX ENTER to choose the matrix A. If you were using another matrix,

you would choose the number of that matrix, for example, 2 for matrix B, and so on.

5. Press ) to close the parentheses. You should see ” det(A) ” on the screen.

6. Press ENTER to evaluate the determinant.

Example:

2 9 7

and find the determinant.

12

SOLVING INEQUALITIES GRAPHICALLY TI-83

1. The intersection-of-graphs method

Then, find the point of intersection using the ”Intersect” option.

2. The x-intercept method

First subtract the terms of the right side from both sides of the inequality so that

only

find the

x-intercept of the graph using the ”Zero” option.

3. Compound Inequality

1

Solve each inequality using the procedures described on previous page.

Now , find the intersection of the two lines using the ”INTERSECT” option. The

solution

x-intercept

From inspection, we see that the line lies below the x axis for x values to the

You must graph in a window in which all 3 lines appear and in which the intersection

points appear. For this example, set the window to [ -15 , 15 ] by [ -20 , 25 ] .

Find the lower intersection point using the ”INTERSECT” option. Note that this

10.283

17

for x values between -1 and 10.283. So, the solution set is ( -1 , 10.283) .

18

EVALUATING RADICALS TI-83

You should enclose the radicand of the radical in parentheses. The square root

and the cube root options automatically supply the open parenthesis immediately

following the radical sign. Take care to close the parentheses in the appropriate place.

1. Square root

The answer is 2.853347622

not

part of the radicand.

2. Cube root

The cube root is located under the MATH menu, option 4.

Press MATH 4 1 5 ) ENTER

The answer is 2.466212074

1

3. Other roots

To access 4th roots and higher, you go to the MATH menu and select option 5.

However, you must supply the index of the radical before selecting the option from

the MATH menu.

Press 5 MATH 5 3 2 ENTER

The answer is 2 .

The parentheses are not automatically supplied for 4th roots and higher, so in this

The answer is 6.411119836

4. Rational Exponents

Since eponentiation has a higher priority than division, you must enclose a

rational exponent in parentheses.

The answer is 7.120367359

2

Exercises : Evaluate the following expressions and round the answer to

4 decimal places.

3

Answers:

1. -4.5947

2. 4.0738

3. 1.5812

4. 10,763.6518

5. nonreal answer if calculator is in ”REAL” mode or

6. .1314

3

7. 2.1611

8. 34.5632

4

QUADRATIC FORMULA PROGRAM TI-83

To create a program, press PRGM , move cursor over to NEW and press ENTER

.

Type in the name of the program ( the calculator is locked in ”alpha” mode so that

when

you press a key, the corresponding letter is accessed). You can name this program

QUAD.

When you type in the name of the program, press ENTER and you are ready to

begin

typing in the actual program. Each line of the program begins with a colon.

Below is the way the program looks on the calculator and the keystrokes for that line.

PROGRAM KEYSTROKES

ENTER

ENTER

ENTER

0

ENTER

1

:Goto 1 PRGM 0 1 ENTER

ALPHA

STO ALPHA 8 ENTER

ALPHA

STO

ALPHA 8 ENTER

:Stop PRGM ALPHA COS ENTER

:Lbl 1 PRGM 9 1 ENTER

is the multiplication sign, not the variable x.

:Stop PRGM ALPHA COS ENTER

To leave the program, press 2nd MODE .

2

To use the program, press PRGM , choose the number of the program, and press

ENTER . You then enter the values of a, b, and c from the equation.

Examples:

3