Graphing Calculator
Graphing with the TI-85
I.
Introduction
The TI-85 has fifty keys, many of which will 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 to
2
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 blue 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 (blue) key.
II.
Entering an equation
Begin by pressing the GRAPH key. The GRAPH menu appears
on the screen and gives the following options: y(x)=, RANGE,
ZOOM, TRACE, GRAPH. These options are accessed by
pressing the F keys located in the top row of keys. Notice the
arrow to the right of GRAPH on the screen. This arrow indicates
there are more options. Note: the x and y-axes may appear on the
screen. If they do, ignore them for now.
Press the MORE key to see more on-screen menu options. Notice
the arrow to the right of the RCGDB menu option. This means
there are even more options.
Press the MORE key to see the remaining menu options.
Press MORE again to return to the original menu options.
Select y(x)= by pressing F1. 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 y1 = use the
key to move the cursor to the line
containing the expression and press CLEAR. Repeat as needed.
MLC/CN/Su ‘04/02/17/06
MLC MTH 070 Graphing With the TI-85
Now with the cursor at y1 = enter 2x+5. Use the x-VAR key or F1
to enter the variable x.
III. Displaying Values in a Table
To create a table with the TI-85 you must have the TABLE
program loaded onto your calculator. See an instructor if you do
not have the TABLE program. Once the program is loaded onto
your calculator press the PRGM button.
Press F1 to access the on-screen NAMES menu option. This will
display the names of all the programs that have been loaded onto
your calculator in alphabetical order. You may have to press the
MORE button a few times to find the table program.
Press F1, ENTER
Press F1 if you want to produce a table for one equation or F2 if
you want to produce a table for 2 equations. For this example
press F1.
TblMin is the first input value in the table. Enter –2 for for
TblMin and press ENTER. Be sure to use the (-) button for the
negative.
∆Tbl is the increment for the input values. Then enter 3 for ∆Tbl
and press ENTER.
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. Use the F1 and F2 keys to scroll through the
table a page at a time and use the F3 and F4 keys to scroll through
the table a line at a time. Press F5 to quit using the program.
MLC/CN/Su ‘04/02/17/06
2
MLC MTH 070 Graphing With the TI-85
IV. Graphing an Equation
Press M3 (2nd, F3) to select the ZOOM menu, then select ZSTD
by pressing F4.
You should get the graph of y = 2x + 5 . The ZSTD 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 F2 to get RANGE. This is the RANGE
screen. 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.
Press TRACE (F4). The calculator places the cursor on the graph
of the line y = 2x + 5 . The number 1 in the upper right corner of
the screen indicates the number of the equation being traced, y1 in
this example. 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= .
V.
Finding the Points of Intersection of Two Graphs
Now, in the Y= screen (press GRAPH, y(x)=), enter the equation
or
y2 = x 2 . To get the cursor next to y2 = press either
2
ENTER. For the x symbol you must press x-VAR or F1 then the
x 2 key.
To see the graph press GRAPH (2nd, F5). Now press TRACE
(F4). The cursor starts out at the point (0, 5) on the graph of y = 2x
+5. Practice moving the cursor along the line using and .
Move the cursor to the graph of y = x 2 by pressing
or .
Notice the equation number is indicated in the upper right
corner of the screen. You can move back and forth between
graphs using
or
. There is one point on the screen
where the two graphs cross. We can use the calculator to
determine the coordinates of this point of intersection.
MLC/CN/Su ‘04/02/17/06
3
MLC MTH 070 Graphing With the TI-85
To approximate the point of intersection you can use TRACE to
move the cursor to the point of intersection. To get a better
approximation, take a closer look at the graph using the ZOOM
BOX feature. Press GRAPH, ZOOM (F3) then BOX (F1). This is
the BOX or ZOOM BOX option.
ZOOM BOX lets you draw a box then enlarge it. Use , , ,
and to move the cursor. When the cursor is where you want the
upper left corner of the box to be press ENTER.
Use , , , and to form the sides of the box. Draw the box
so that the point of intersection is enclosed. When the cursor is
where you want it press ENTER.
What was inside the box now fills the screen. You can use TRACE
to approximate the point of intersection. BOX and TRACE may be
repeated to find increasingly accurate coordinates for the point of
intersection.
Press RANGE (M2) to see how the calculator changed the
window size to make the zoom occur. Press ZOOM then ZSTD to
get back to the standard window. You can verify that you are back
to the standard screen window by pressing RANGE (F2).
Another method for finding a point of intersection is to use the
intersection feature of the calculator called ISECT. Press MORE,
then MATH (F1).
Now press MORE, ISECT (F5). The cursor appears on one of the
graphs. You can tell which one by looking at the number in the
upper right corner.
Press ENTER to indicate that the cursor is on one of your curves.
The cursor jumps to the other graph.
MLC/CN/Su ‘04/02/17/06
4
MLC MTH 070 Graphing With the TI-85
Use the , and keys to move the cursor close to the point of
intersection and press ENTER.
The cursor jumps to the point of intersection and the coordinates
of that point are indicated along the bottom of the screen.
VI. Finding the x-intercepts of a graph
Clear the previous equations and enter the equation y = x 2 − 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 MORE then MATH (F1).
We are looking for the x-intercepts of a quadratic, which are also
called roots. Press ROOT (F3). We will find the x-intercepts
separately. Notice that the cursor is flashing on the screen at the
point (0,-6). Use the to move the cursor near the leftmost xintercept and 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 process to find the other x-intercept.
MLC/CN/Su ‘04/02/17/06
5
MLC MTH 070 Graphing With the TI-85
6
VII. Problems for Practice
Use a calculator to make a table of values for the following equations. Use TblMin=−10
and ∆Tbl=5
1. y = 3x + 2
2. y = 23 x + 4
Use a calculator to draw the graphs of the following equations.
3. y = 3(2 − x)
4. y = 5 + 2(x − 1)
5. Find the point of intersection of the graphs of y = 5(x + 1) and y = −2(x + 3)
6. Find the x-intercepts of y = x 2 + 3.9 x − 2.7
Answers: (standard window)
1.
2.
4.
5.
6.
MLC/CN/Su ‘04/02/17/06
3.