Graphing Calculator
Graphing with the TI-83 Plus/TI-84 Plus
I.
Introduction
The TI-84 Plus graphing calculator has greater memory capacity, is faster, and has a higher
contrast screen than the TI-83 Plus model. Aside from these differences, the two calculators have
virtually the same keyboards and they are keystroke-for-keystroke compatible. This is also true of
the older TI-83 and TI-84 models. All TI-83 and 84 models have fifty keys, many of which
perform multiple functions when used in combination. Each key has a symbol printed on its face.
When a key is pressed the calculator does whatever is printed on the face of the key. This is often
referred to as the primary function of the key. For example, the primary function of the ON key is
2
to turn the calculator on, the + key performs addition, and x raises numbers to the second power.
In addition to their primary functions many keys have second, or shifted functions. These
are the symbols written in yellow and green above the keys. To have the calculator do what is
written in yellow you must first press the 2nd (yellow) key. To type letters into the calculator you
must first press the ALPHA (green) key.
II.
Plotting Points in a Scattergram
We can use the calculator to create a scattergram of the data displayed in the
table at right. As you follow the steps below, compare the screen on your
calculator to the screenshots to the right.
Press the STAT key. Your calculator window should look like the picture
at the right.
Press 1 (Edit). If you have any numbers (data) in the lists (L1, L2, or L3,
etc.) you can clear them by pressing the up arrow
to move the cursor to
the top of the column, then press the CLEAR key, followed by ENTER.
Use
or
to get to the next list, and repeat the steps to clear all the lists.
NOTE: if you press DEL instead of CLEAR, the entire column will vanish. If you do this
by accident, pres STAT 5 (SetUpEditor) then ENTER to replace the deleted column.
To enter the new data, press the STAT key, then 1 (Edit). Enter the Xvalues from the table in L1 by typing 2 ENTER, 5 ENTER, 8 ENTER, 11
ENTER. Move the cursor to L2 and enter the Y-values; 25, 28, 58, and 130
in the same way.
Now press the Y= key. If you have any equations on this screen, press
CLEAR. Use the
and
keys to move from Y1= to Y2= and Y3= etc.
and press CLEAR to remove all equations.
Next, press 2nd then STAT PLOT.
x
2
5
8
11
y
25
28
58
130
MLC MTH 070 Graphing With the TI-83/TI-84
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Press 1 to select Plot 1, then Press ENTER to turn Plot 1 on. Note that
Type, Xlist, Ylist, and Mark should all be set the same as the picture at the
right. The Type shown is scattergram , the data list uses L1 for the Xvalues, L2 for the Y-values, and the points will be plotted as little squares as
indicated by Mark.
Finally, to see the scattergram, press ZOOM, then press ZoomStat (9).
ZoomStat automatically adjusts the calculator window so that all the points
in the scattergram are visible.
III. Entering an equation
We use the top row of keys for graphing, they are:
Y=
WINDOW
ZOOM
TRACE
GRAPH
Start by pressing Y=. The flashing rectangle next to \Y1= is called the
cursor. The cursor indicates where characters will appear when a key is
pressed. If there are expressions next to any of the \Y=, use the
to
move the cursor to the line containing the expression and press
CLEAR.
Now with the cursor at \Y1= enter 2x + 5. Use the X,T,θ,n key to enter
the variable x.
IV. Displaying Values in a Table
We can use a calculator to display a table of values for an equation that
has been entered into the calculator. Press 2nd then TBLSET (the
WINDOW button) to set up the table. TblStart is the first input value
in the table and ∆Tbl is the increment for the input values. Enter −2 for
TblStart (be sure to use the (−) key) and press ENTER. Then enter 3
for ∆Tbl and press ENTER.
Press 2nd then TABLE (the GRAPH button). Notice that the x values
start at −2 and increase by an increment of 3. These are the instructions
that you gave the calculator in the previous window. You can scroll up
or down the table using
or .
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MLC MTH 070 Graphing With the TI-83/TI-84
V. Graphing an Equation
Press ZOOM. Notice there are many options under the ZOOM menu.
Select ZStandard by pressing 6. You should get the graph of
y = 2x + 5. The ZStandard command tells the calculator to graph the
equation in the standard screen.
The standard screen includes the x-axis from –10 to +10, and the y-axis
from –10 to +10. Verify this by pressing WINDOW. Xscl=1 means the
x-axis is scaled so that each mark is one unit. Notice the y-axis is also
scaled with one mark representing one unit. Xres=1 is the resolution
setting and should usually be left at 1.
Press TRACE. The calculator places the cursor on the graph of the line
y = 2x + 5 . The equation written in the upper left corner of the screen
indicates what equation has been graphed. Move the cursor along the
line by pressing
or . Notice at the bottom of the screen the
coordinates of the cursor are indicated by X = and Y= .
VI.
Using “Intersect” to Solve an Equation.
We can use the “Intersect” feature on the calculator to solve the equation
3x − 7 = 5 . In the Y= screen, enter the equation \Y1 = 3x − 7 and \Y2 = 5 .
To see the graph, press GRAPH. Notice the graph of Y1 is a straight line
with a slope of 3 and the graph of Y 2 is a horizontal line. Press 2nd,
then CALC (F4).
To find the point of intersection of the two lines, press intersect (5).
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MLC MTH 070 Graphing With the TI-83/TI-84
4
The cursor appears on one of the graphs. You can tell which one by
looking at the upper left corner. The calculator prompts you to tell it
which two graphs (curves) you are finding the intersection of. Press
ENTER to indicate that the cursor is on one of your curves.
The cursor jumps to the other graph and prompts you with “Second
curve?”. Press ENTER to indicate that the cursor is on the other curve.
Now the prompt is “Guess?”, which is asking you to place the cursor
near the point of intersection. Use the , and keys to move the
cursor close to the point of intersection.
Press ENTER. The cursor jumps to the point of intersection and the
coordinates of that point are indicated along the bottom of the screen.
VII. Linear Regression
Using the data in the table at the right, we’ll use the calculator’s linear
regression feature to find a linear equation that best fits the data. First, we
need to enter the data into the stat lists. If you need to refresh your memory on
how this is done, go to section II of this supplement and follow the first four
steps of “Plotting Points in a Scattergram”.
When the data has been correctly entered your screen should look like
the picture at the right.
To perform the linear regression function, first press the STAT key.
We want to perform a calculation on the data, so press the right arrow
to CALC.
MLC/TM/Su ‘08/09/26/08
x
2
5
8
11
y
25
28
58
130
MLC MTH 070 Graphing With the TI-83/TI-84
Select LinReg (4) to perform a linear regression. Note there are other
types of regression besides linear. In this window the options include
quadratic regression (QuadReg (6)) and exponential regression (ExpReg
(0)) among others.
Press ENTER to perform the regression. This output describes a linear
equation with slope 11.5 and y-intercept -14.5, so the equation is
y = 11.5 x − 14.5 . We are not going to use the r 2 = or r = for our
purposes. Don’t worry if your calculator does not show these values.
To graph the regression equation along with the scattergram, first plot
the scattergram by turning on plot 1 and pressing ZOOM then
ZoomStat (9). If you need to refresh your memory on these steps, go to
section II, “Plotting Points in a Scattergram”, and read steps 5 through
10.
Press Y=. Be sure that all equations are cleared and the plot is turned on.
When we perform regression, the equation is stored as a statistics
variable named RegEQ. We graph the regression equation by inserting
RegEQ into the y= window. First, to find RegEQ, press the VARS key.
Since RegEQ is a statistics variable, select Statistics (5) by pressing 5.
RegEQ is an equation, so select EQ by pressing the right arrow twice
.
Select RegEQ by pressing 1 (or ENTER). This inserts the regression
equation into the y= screen for graphing.
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MLC MTH 070 Graphing With the TI-83/TI-84
Press GRAPH. We can see the regression line along with the
scattergram of the data.
VIII. Finding the x-intercepts of a graph
Turn off plots and clear the previous equations and enter the equation
y = x2 − x − 6 .
Graph the equation. Be sure the window is set so that you can see all of
the x-intercepts. In this example use the standard window.
Press 2nd then CALC (the TRACE button). The menu under
CALCULATE has several options. We are looking for the zero values
so press 2.
The cursor is flashing on the graph at the point (0,−6). The calculator
will only look for one x-intercept at a time and it will only look for one
within a range of x values that you must specify. Left Bound? on the
screen is a prompt for you to enter the smallest x value in the range.
to move the cursor to the left of the leftmost x-intercept and
Use
press ENTER. The right-pointing black triangle on the screen
indicates the smallest x value the calculator will consider in looking for
an x-intercept. Right Bound? on the screen is a prompt for you to
enter the largest x value in the range.
to move the cursor to the right of the leftmost x-intercept and
Use
press ENTER. The left-pointing black triangle on the screen indicates
the largest x value the calculator will consider in looking for an xintercept. You should have placed the left and right bounds to that
there is one and only one x-intercept between the triangles horizontally.
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MLC MTH 070 Graphing With the TI-83/TI-84
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Guess? is a prompt for an x value in the specified range that the
calculator can use to start its search algorithm. Any x-value in the
range will work. If you press ENTER the calculator will use the x
coordinate of the current position of the cursor. Since the cursor is at
the right bound, that value is valid. Press ENTER. The cursor is
flashing on the x-intercept and its coordinates are listed at the bottom of
the screen: (−2,0).
Repeat the procedure to find the other x-intercept.
IX.
Problems for Practice
Use a calculator to make a scattergram of each of the following data tables.
1.
2.
x
y
1
7
7
50
15 101
25 190
x
2
5
8
11
y
25
28
58
130
Use a calculator to make a table of values for the following equations. Use TblStart=−10 and
∆Tbl=5
4. y = 23 x + 4
3. y = 3x + 2
Use a calculator to draw the graphs of the following equations.
5. y = 3(2 − x)
6. y = 5 + 2(x − 1)
7. Use the “Intersect feature to solve the equation; 2 x − 3 = 4
8. Find the point of intersection of the graphs of y = 5(x + 1) and y = −2(x + 3)
9. Use linear regression to find a model of best fit (equation) for each of the tables. Graph the
regression model and the scattergram in the same window. Round decimals to two places.
a)
b)
x
y
x
y
1
7
2
25
7
50
5
28
15 101
8
58
25 190
11 130
10. Find the x-intercepts of y = x 2 + 3.9 x − 2.7
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MLC MTH 070 Graphing With the TI-83/TI-84
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Answers: (standard window)
1.
2.
3.
4.
5.
6.
7. x = 3.5 , y = 4
8.
10.
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9. a) y = 7.55 x − 3.59
b) y = 11.5 x − 14.5