An Algebra II Student’s Guide
to the
TI-84+ Graphing Calculator
prepared by:
Mrs. P. Marques
Seneca High School
Welcome to Algebra II! This guide is intended to assist you as you use your
graphing calculator throughout the course. Your teacher will require you to be able to do
many problems both with and without the graphing calculator.
CONTENTS
1. Getting Started ........................................................................................................................ 1
2. Order of operations .................................................................................................................2
3. Graphing a line ...........................................................................................................................3
4. Adjusting the viewing window.................................................................................................3
5. Finding x-intercepts of a linear function ...........................................................................4
6. Scatter plots and lines of best fit ......................................................................................5
7. Solving a system of linear equations ...................................................................................7
8. Entering matrices ..................................... ..............................................................................8
9. Finding x-intercepts of a quadratic function ...................................................................9
10. Finding the vertex of a quadratic function .....................................................................9
11. Solving polynomial equations ................................................................................................10
12. Permutations and combinations ..........................................................................................11
13. Evaluating rational exponents ............................................................................................12
14. Finding nth roots ....................................................................................................................12
15. Absolute value ........................................................................................................................12
16. Technical Support .................................................................................................................13
GETTING STARTED
Whether you are using a TI-84+ or a similar graphing calculator, keep in mind that
every function is color-coded. Below is an image of the TI-84+ taken from the following
website: 21ctf.fi.ncsu.edu/msms/ti84.html.
In order to use the blue functions listed above the keys, you must first press the
blue “2nd” key. In order to access the light green letters and functions listed above the
keys, you must first press the light green “ALPHA” key.
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ORDER OF OPERATIONS
You must understand and know the order of operations in order to evaluate an
1  2  32
expression correctly using your calculator. To evaluate the expression
, you must
2(8)
remember that the division bar (vinculum) groups the numerator and denominator, so the
equation must be entered with parentheses grouping the numerator and parentheses
grouping the denominator in the following way:
(
1
)

)
ENTER
(
2
+
3
x2
2
(
8
)
If you want the answer to be in the form of a fraction, you can access this function
by pressing the MATH key at the end of your expression. You can also avoid retyping an
expression by recalling it using the 2ND ENTER keys.
2ND
ENTER
MATH
ENTER
ENTER
Keep in mind that the TI-84+ family of graphing calculators will only display reduced
fractions in either proper or improper form.
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GRAPHING A LINE
In order to graph a line, you must solve it for y . To graph the line 3x  4 y  8 , you
3
must first rewrite it as y   x  2 before you enter it into the calculator.
4
Y=
(
+
2
(-)
3

4
)
x,T,  ,n
In order to graph the line in a standard viewing window
where the x-axis runs from -10 to 10, and the y-axis runs
from -10 to 10, press the
the above key strokes.
ZOOM
6
keys after entering
NOTE: You can always return to the home screen at any
time by pressing 2ND MODE .
ADJUSTING THE VIEWING WINDOW
Let’s say that when you graph the line you cannot see its x- or y-intercepts on the
screen. In that case, you must press the WINDOW key in order to adjust the window. For
example, if you want to graph the line y  15x  27 you would see:
Go to WINDOW to change
what you see on the screen.
Since you know that the yintercept is 27, you need only to
adjust the Ymax entry to a
number larger than 27.
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Press GRAPH . Now you can
see the graph and both of its
intercepts.
There is no specific method to follow in order to adjust the viewing screen window.
Sometimes you just have to make educated guesses when changing the maximum and
minimum values.
FINDING X-INTERCEPTS OF A LINEAR FUNCTION
In order to find the x-intercepts of a line on the graphing calculator, you must first
graph the line as outlined above. Using the line y  15x  27 from the previous example,
let’s find the x-intercept.
Start by pressing 2ND
Note that a
“zero” is equivalent to an “xintercept” in mathematics.
TRACE
2
.
The calculator will ask you for
a left and right bound. This simply
means that you should enter a
number you think is to the left of
the x-intercept and one that is to
the right. Just type in these
numbers as you are given the
prompts. Here, you simply press
(-)
When the calculator asks
you to guess, simply take your
cursor close to the point of
intersection.
5
ENTER .
Finally, press ENTER to
view the answer displayed at
the bottom of the screen. The
x-intercept is at x = -1.8.
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0
ENTER
SCATTER PLOTS AND LINES OF BEST FIT
When you are given a list of data, you can graph it on you calculator. Let’s say you
were given the following information:
x
y
1
2
3
4
5
6
7
8
9
10
11
-2
2
5
1
6
10
3
5
5
12
9
You must enter this information into your calculator by creating lists for your
information.
Press the STAT key and
select option 1.
You will enter the x values in
L1 and the y values in L2. This is
done by taking your cursor to the
top of each list and typing in the
number followed by the
ENTER key. You will do this for
each number entered. To move
onto the next list simply move
your cursor over to that column
and repeat the steps.
Once your lists are
entered, press 2ND
Y=
to access the STAT PLOT
function. Press ENTER to
select Plot 1.
NOTE: You may need to
Use the cursor keys to
navigate through the different
selections on the screen. Press
ENTER to select an option.
Finally, press GRAPH .
adjust the viewing window to
see a better picture of your
scatter plot. Also, if there are
other graphs on your viewing
screen, press
Y=
and clear
any equations you may have.
However, if you need the
equations in the Y= screen for a
later date, you can simply deactivate them by placing the
cursor on the equal sign and
pressing ENTER . This allows you
to keep the equations, but they
won’t be graphed.
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To find the equation of the
line of best fit, press STAT
and move the cursor over to
CALC and select option 4.
Press the GRAPH key and
you will see the scatter plot
graphed along with the line
of best fit.
Then press 2ND
1
,
,
2ND
2
VARS and move the cursor over
to the Y-VARS option and select
option 1. Finally, select option 1
again for Y1. What this allows
you to do is to get the line of
best fit and have it pasted to
your Y= screen. Press ENTER to
get the line of best fit.
(If you press Y= , you will
notice that the regression
equation you just calculated is in
Y1.)
Notice that the values for
a and b are given. The value
of r is the correlation
coefficient. The closer the
value is to 1, the closer the
plotted points are to the line
of best fit. If you do not
see the value for r, do the
following:
x 1
and
scroll down until you find
DiagnosticON. Press ENTER
twice and repeat the steps
in the previous column.
2ND
0
NOTE: If you return to the
Y=
screen, you will
notice that PLOT1 is highlighted at the very top. It
is important to turn all plots off in order to be able
to graph equations entered in the
Y=
. You do
this by moving your cursor up to the highlighted plot
and press ENTER in order to remove the highlight.
This can also be done by pressing 2ND
Y=
and
going into each of the plots to turn them off in the
same way you turned them on. If you don’t turn off
the plots, your equations will always be graphed
together with the scatter plot or you may get an
error message.
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SOLVING A SYSTEM OF LINEAR EQUATIONS
When you solve a system of linear equations, you are finding the point of
intersection of that system. First you need to graph the lines and ensure that you can see
the point of intersection on the screen by adjusting the viewing window as necessary. In
 7 x  12

order to find the point of intersection for the linear system  2
, you would do the
 3 x  15
following:
Enter the equations into the
calculator.
Graph it on the standard
viewing window. Since you can’t
see the point of intersection,
adjust the window.
Now that you can see the
point of intersection, press
2ND
TRACE
5
Notice that the point of
intersection is in quadrant IV.
Use this fact to help you choose
the max/min values and graph the
lines again.
The calculator will ask you
which curves (lines) you want to
find the intersection of. The top
of the screen displays one of the
equations we want. Press ENTER .
ENTER
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The second line we want is
displayed on the top so press
ENTER .
Here, you may just want to
move your cursor to the point of
intersection although this is not
necessary. Press ENTER .
You can now see that the point
of intersection of the linear
system is approximately at
(3.5, -12.7) .
ENTERING MATRICES
3  7 12 
 into the calculator, follow the steps
0 9  4 
In order to enter the matrix 
below:
1
Press
2ND
and move the
x
cursor over to EDIT. Select an empty
matrix and press ENTER .
Use the cursor keys to enter the
dimensions of the matrix. Then press
ENTER after you type in each entry. To return to
the home screen press 2ND
MODE .
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FINDING X-INTERCEPTS OF QUADRATIC FUNCTIONS
You can find the x-intercepts of a quadratic function in the same way as you did
when finding the x-intercept of a line.
Enter the equation into the
Press 2ND TRACE
2
calculator by going to the
Y=
and follow the prompts as you did
screen. Graph the equation in the for finding the x-intercept of a
standard viewing window and
line.
adjust the window as necessary.
One x-intercept is at about
x = -1.9. To find the other xintercept, follow the same steps
as before. When the calculator
asks for a guess, simply move the
cursor closer to the other xintercept you want to find.
The other x-intercept is at
about x = 1.2.
FINDING THE VERTEX OF A QUADRATIC FUNCTION
The vertex of a parabola is either its maximum or minimum point. The vertex of the
above parabola is a minimum and can be found by pressing 2ND TRACE 3 .
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Once the graph appears on the
Because the vertex appears to
x = 2 appears to be to the
screen, follow the left/right
be at about (0, -7), the choice of right of the vertex so it is a good
bound prompts as you did before. x = -2 for a left bound seems
choice for the right bound.
appropriate.
NOTE: In order to find the vertex of a
parabola which is a maximum, follow the
previous steps, but select option 4 (maximum)
in the CALCULATE screen.
When the “Guess” prompt
appears, simply press ENTER .
The vertex is at (-0.3, -7.3).
SOLVING POLYNOMIAL EQUATIONS
Suppose you are asked to solve the polynomial equation 3x 3  7 x 2  5x  7  10 . If you
tried to set the equation to zero and factor, you would find that this would be impossible.
It is only possible to solve using the graphing calculator. Follow the steps below:
Enter the left side of the
equation into Y1 of the Y=
screen. Enter the right side as
Y2.
Graph the equations. It may
be necessary to adjust the
viewing window.
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Press
2ND
TRACE
5
.
Answer the prompts as you did
The second point of
when solving a system of linear
intersection is at about (-0.4, 10)
equations. Remember to move
the cursor to the desired point of
intersection each time the
prompt asks you to “guess.” The
first point of intersection is at
about (-2.8, 10).
The last point of intersection
is at about (0.9, 10)
From these three points of
intersection, we can determine
that the solutions to the equation
3x 3  7 x 2  5x  7  10 are at
about x = -2.8, x = -0.4, and
x = 0.9.
PERMUTATIONS AND COMBINATIONS
The permutation and combination keys can be accessed by pressing the MATH key.
You will need to use your arrow keys to highlight the PRB heading. In this screen, you can
now access the permutation function (option 2), the combination function (option 3), and
the factorial function (option 4).
To compute 5P3, for example, press
5
MATH and arrow over to PRB. Then press
2
to select option 2. Finally, press
3
ENTER .
Follow the same steps to find a combination selecting option 3 instead.
-11-
EVALUATING RATIONAL EXPONENTS
To evaluate 243 5 simply
press 2
4
^
(
3
)
/
5
ENTER .
FINDING nth ROOTS
To evaluate 5 86 simply
press 5
MATH
5
8
6
ENTER .
ABSOLUTE VALUE
To evaluate 2(3)  10
using the graphing
calculator, press MATH and
arrow over to NUM. Select
option 1 by either pressing
1
or ENTER . Type in
the rest of the quantity
remembering to end with
)
. Press ENTER .
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TECHNICAL SUPPORT
If you are having trouble using your calculator, your teacher is a good source of
information. Others in your class may also be able to help you. If you have a technical
problem with your graphing calculator call 1-800-TI CARES. Texas Instruments has
fantastic technical support and can take you step by step in solving your problems.
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