TI – 84 Plus
Tips and Techniques
Kenneth Mann
Modified by Terry Dugger for Math 080
Catawba Valley Community College
Revised Spring 2008
2
Part I Standard Commands
1. Operations
2. Exponent key
3. Square key
4. Square root key
5. nth root key
6. Fractions
7. Enter key
8. Scientific notation
9. Reset
p. 3
p. 3
p. 3
p. 3
p. 3
p. 3
p. 3
p. 3
p. 4
Part II Graphing
1. Linear equations
2. Quadratic equations
p. 4
p. 5
Part III Working with Graphs
1.
2.
3.
4.
5.
6.
7.
8.
How to set up your table
How to find the x-intercept
How to find the y-intercept
How to find the intersection of two lines
How to find the intersections of two curves
How to find y when given x
How to find x when given y
How to solve a system of equations
p. 5
p. 5
p. 6
p. 6
p. 6
p. 7
p. 7
p. 8
Part IV Statistical Commands
1. Plotting points
2. Graphing line graphs
3. Linear regression to graph
4. Predictions
5. Linear regression for equation
6. Double Linear Regression
7. Double Linear Regression –
Graphing the Lines Only
p. 8
p. 9
p. 10
p. 11
p. 12
p. 13
p 14
Foreword: This is by no means a complete list of everything the TI-83/84 can
do. This is intended to get you through the basics of the topics listed above. I
would recommend the TI web site http://education.ti.com to see more
applications of the calculator. Also, this text is geared for the TI – 83/84, TI –
83/84 plus, and the TI – 83/84 plus silver edition only. And while calculators
make excellent tools and are efficient time savers for the most part, there is
seldom a substitute for learning and doing things “by hand”.
Note: Keys to be pressed will be in italics.
3
Part I Standard Commands
1. Addition, subtraction, multiplication, and division are the same as on a
scientific calculator.
2. The power key is ^, located on the right side above the division key.
3. The square key (x2) is on the left side 4 keys up from the on key.
4. To get the square root key hit 2nd, x2, and the number you are taking the
square root of.
example. 2nd, x2, 16 You should see 16 after you finish typing.
Hit Enter to get 4.
Note: It is not necessary to close parentheses but it is not a
bad habit to get into.
5. nth root
To find the 4th root of 16: Press 4, press Math, select # 5, type in 16 then
press enter. The answer is 2.
6. Converting numbers to fraction form.
a. You can type in the number, then press Math. You will see the word Math
on the top of the screen highlighted, then immediately below it you will
see 1: > Frac with the 1: highlighted. Hit Enter twice and the original
number will be in fraction form.
Note: Not all numbers will be converted into fractions if they are
irrational numbers or numbers with large denominators.
b. If you have performed calculations and wish to convert an answer to
fraction form, after you have gotten your final answer hit Math, then
Enter twice, and you will see your answer as a fraction.
c. To type in a fraction press Alpha F1, which is the Y= button. Select1 or
n/d. Put in the numerator and then press the down arrow and put in the
denominator. Hit the right arrow to exit the fraction.
7. If you wish to see a previous calculation hit 2nd and Enter, and you will
see the last calculation you performed. You can scroll to edit what you
typed if need be. If you hit 2nd and Enter again you will see the
calculation before last, and so on. If you go too far eventually you will
come back to the most recent operation.
8. A number written with E and a number after it (example: 2.999999E12)
is written in scientific Notation. The equivalent form would be the first
4
number multiplied by 10 to the 12th power. A number written as 4E-7 is 4
multiplied by 10 to the – 7th power (a decimal point, 6 zeroes, and a 4 or
0.0000004)
9. To reset the calculator.
Press 2nd Mem, this is the plus key, select # 7 Reset, select #1 All RAM,
select 2 Reset.
Warning: this will erase any programs that you have added to the
calculator.
Part II Graphing
1. Linear equations
To graph a linear equation
1. Hit “Y=” in the upper left corner. The cursor will be next to “=” next to Y1.
2. Type in the equation using the “X,T,  ,n” key below the “mode” key at
the top of the calculator. Note that the equation should be in slope –
intercept form (in the form y = 3x + 5 for example).
3. A “standard window” has the following characteristics.
Xmin = - 10
(the minimum x – value on the screen will be – 10)
Xmax = 10
(the maximum x – value on the screen will be 10)
Xscl = 1
(the marks on the x – axis will be 1 unit apart.)
Ymin = - 10
(the minimum y – value on the screen will be – 10)
Ymax = 10
(the maximum y – value on the screen will be – 10)
Yscl = 1
(the marks on the y – axis will be 1 unit apart.)
Xres = 1
Note: You can set your calculator to a “standard window” by pressing
Zoom and choosing 6 for zstandard.
4. To see the equation and the x and y coordinates of the cursor hit trace
and they will appear.
5. To find the y-intercept see p 5.
6. To find the x-intercept see p 5.
Examples: Graph the following equations:
Y = -3x + 23
Y = 2/3x - 6
5
2. Quadratic equations
1) Quadratic equations are graphed the same as linear equations.
2) The X-intercept and the Y-intercept are found the same as linear
equations.
Note: Quadratic equations usually have more than one
X-intercept.
Examples:
Graph: y = 2x2 + 5
Part III Working with Graphs
1. How To Set up Your Table
1. Press 2nd Table Set, this is above the window key
2. Set the indpnt to ASK
3. Set the depend to AUTO
2. To find the x-intercept
1. Put the equation in Y1.
2. Put the zero in Y2
3. Graph. Make sure you have the intersection on the screen.
4. Press 2nd CACLULATE
5. Select #5: intersect
6. “First curve” appears on screen
7. Press ENTER
8. “Second curve” appears on screen
9. Press ENTER
10. “Guess” appears on screen
11. Press ENTER
12. “x = ________
y = ________” appears at bottom of
the screen. This is the point of intersection.
13. The x value is your answer
6
3. To find the y-intercept.
1. Put the equation in Y1.
2. Press 2nd TABLE
3. Put zero in for x
4. The y intercept will appear in the Y1 column.
4. To find the intersection of two lines
1. Put the first equation in Y1.
2. Put the second equation in Y2
3. Graph. Make sure you have the intersection on the screen.
4. Press 2nd CACLULATE
5. Select #5: intersect
6. “First curve” appears on screen
7. Press ENTER
8. “Second curve” appears on screen
9. Press ENTER
10. “Guess” appears on screen
11. Press ENTER
12. “x = ________
y = ________” appears at bottom of
the screen. This is the point of intersection.
13. The x value is your answer
Example: Find the intersection or solution of the following equations:
Y = 2x + 12
Y = -4x + 3
Solution is (-1.5, 9)
5. To find the intersection between a line and a curve or 2 curves
1. Finding the first intersection is the same as finding the intersection of 2
lines. (see above)
7
2. Finding the second intersection is like finding the first, except you must
guess, placing the cursor closer to the second intersection than the
first.
Examples:
Find the intersection between:
Y = x2 – 6
Y = 2x + 2
6. To find the y – value for a given x – value when given an equation.
1. Hit Y = to enter an equation. You may need to rewrite the equation to get
y by itself first before you enter it in.
2. Hit 2nd Table Set. Move your curser to the “Ask” beside the Independent.
Press enter to highlight the Ask. Beside the dependent you should have the
Auto highlighted.
3. Hit 2nd Table. Under the x, input the x value and the y value will appear in
the Y1 column.
7. To find a x – value for a given y – value when given an equation.
1. Put the equation in Y1.
2. Put the y-value in Y2
3. Graph. Make sure you have the intersection on the screen.
4. Press 2nd CACLULATE
5. Select #5 : intersect
6. “First curve” appears on screen
7. Press ENTER
8. “Second curve” appears on screen
9. Press ENTER
10. “Guess” appears on screen
11. Press ENTER
12. “x = ________
y = ________” appears at bottom of
the screen. This is the point of intersection.
13. The x value is your answer
8
8. To solve a system of 2 equations with 2 unknowns
1) Input the first equation in Y1
2) Input the second equation in Y2
3) Find the intersection. (see p 6)
4) “x = ________
y = ________” appears at bottom of
the screen. This is the point of intersection.
Part IV Statistical Commands
1. Plotting Points
1) Press Y=
Y value in L2
2) Clear any equations
12) Press 2nd STAT PLOT
3) Press STAT
13) Select 1
4) Choose EDIT
14) Highlight ON
5) Highlight L1
15) Highlight DOTS
6) Press Clear
16) For X-LIST: L1
7) Press Enter
17) For Y-LIST: L2
8) Highlight L2
18) Select type of dot
9) Press Clear
19) Press WINDOW
10) Press Enter
20) Set window to match data
11) Enter data
21) Press GRAPH
X value in L1
Example: Graph the following data:
Number
of books
5
8
12
Total
weight
3.5
5
8
9
2. Graphing Line Graphs
1) Press Y=
15) Highlight LINE GRAPH
2) Clear any equations
16) For X-LIST: L1
3) Press STAT
17) For Y-LIST: L2
4) Choose EDIT
18) Select type of dot
5) Highlight L1
19) Press WINDOW
6) Press Clear
20) Set window to match data
7) Press Enter
21) Press GRAPH
8) Highlight L2
9) Press Clear
Example: Make a line graph using
the following data:
10) Press Enter
X value in L1
Years
Experence
1
Yearly
Earnings
$27,000
Y value in L2
5
$32,000
12) Press 2nd STAT PLOT
12
$38,000
13) Select 1
25
$45,000
11) Enter data
14) Highlight ON
10
3. Linear Regression – Graphing Line and Points
1) Press Y=
16) For X-LIST: L1
2) Clear any equations
17) For Y-LIST: L2
3) Press STAT
18) Select type of dot
4) Choose EDIT
19) Press STAT
5) Highlight L1
20) Choose CALC
6) Press Clear
21) Select:
4 for linear regression
7) Press Enter
5 for quadratic regression
8) Highlight L2
6 for cubic regression
9) Press Clear
7 for quartic regression
10) Press Enter
22) Press Alpha
11) Enter data
23) Press F4, the trace button
X value in L1
24) Choose Y1
Y value in L2
12) Press 2nd STAT PLOT
25) Press ENTER again
26) Press WINDOW
13) Select 1
27) Set window to match data
14) Highlight ON
28) Press GRAPH
15) Highlight DOTS
Example: Use linear regression to fine the equation of the line that best fits
the following data:
Years
Experence
1
Yearly
Earnings
$27,000
5
$32,000
12
$38,000
25
$45,000
11
4. TO DO PREDICTION
After doing linear regression:
To find the y value when given the x value:
1) Press 2nd Table
2) Input the x value
3) The y value will appear in the Y1 column.
Example: Predict the salary after 30 years for the previous data.
To find the x value when given the y value:
1. Put the equation in Y1.
2. Put the y-value in Y2
3. Graph. Make sure you have the intersection on the screen.
4. Press 2nd CACLULATE
5. Select #5 : intersect
6. “First curve” appears on screen
7. Press ENTER
8. “Second curve” appears on screen
9. Press ENTER
10. “Guess” appears on screen
11. Press ENTER
12. “x = ________
y = ________” appears at bottom of
the screen. This is the point of intersection.
13. The x value is your answer
Example: Predict when the salary will be $40,000.
12
5. Linear Regression – Just to Find the Equation
1) Press Y=
2) Clear any equations
3) Press STAT
4) Choose EDIT
5) Highlight L1
6) Press Clear
7) Press Enter
8) Highlight L2
9) Press Clear
10) Press Enter
11) Enter data
X value in L1
Y value in L2
12) Press STAT
13) Choose CALC
14) Select:
4 for linear regression
5 for quadratic regression
6 for cubic regression
7 for quartic regression
15) Press Alpha
16) Press F4, the trace button
17) Choose Y1
18) Press ENTER again
19) Press Y= to view the equation
13
6. Double Linear Regression – Graphing Line and Points
1) Press Y=
2) Clear the equations
3) Press STAT
18) Choose EDIT
4) Choose EDIT
19) Leave the data in L1
5) Highlight L1
20) Highlight L2
6) Press Clear
21) Press Clear
7) Press Enter
22) Press Enter
8) Highlight L2
22) Enter data
7) Press Clear
Y value in L2
8) Press Enter
24) Press STAT
9) Enter data
25) Choose CALC
X value in L1
Y value in L2
10) Press STAT
11) Choose CALC
12) Select:
4 for linear regression
26) Select:
4 for linear regression
27) Press Alpha
28) Press F4, the trace button
29) Choose Y2
30) Press ENTER again
13) Press Alpha
31) Press Y= for the equations
14) Press F4, the trace button
32) Press WINDOW
15) Choose Y1
33) Set window to match data
16) Press ENTER again
34) Press GRAPH
17) Press STAT
35) For predictions see page 11