Exploring the Vertex Form of the Quadratic Function
Equipment needs:
• TI83+ calculator with Interactive Graphing installed .
Studying the effect of A, B, and C
1. Press [APPS] and select the Transformation
Graphing by
pressing the number to the left of Interact. Press any key
(except y or
) to install Interactive Graphing.
(Note: If you do not
see the screen illustrated to the far right,
select 2:Continue) 

2. In Func mode, press
to display the y=
editor. Clear any functions that are
listed and turnoff any plots . Enter the general vertex form , Y = A(XB)^{2}+ C of
the quadratic
function . Press
C. 

If
the PlayPause Mode is not selected to the left of Y1 (>), press
until the
cursor is over the symbol and then press
until the correct
symbol is selected.
NOTE: You entered Y=A(XB)^{2} + C in place of Y=A(XH)^{2} + K, which is the
form commonly found
in textbooks, because Interactive Graphing only uses
the coefficients A ,B, C, and D. 
3. Press to display the settings screen for
Transformation Graphing.
As a starting place, set the SETTINGS as pictured. To make these
selections, press This defines the starting values for the
coefficients and the increment by which you want to observe the change
in the coefficients . 

Studying the Effect of B
4. Press 6:Zstandard to display the graph. The graph will show the
pre
selected values of A, B, and C. Both the X and Yaxis range from 10
to 10 with
a scale of 1. 

Press
to cursor down one space and
highlight B=. You will start your study
with the effect of B.
5. Press to increase the value of B by the preselected Step value (1
in this example). The graph is
automatically redrawn showing the effect
of this change on B. Continue to press
until you have an
idea of how
changing B effects the graph.
6. Press to decrease the value of B by the preselected Step value.
Did the graph move the direction
you would have expected?
** Changing the value of B has the curve move in what direction?
This moving of the curve is called a translation in the Xdirection or
horizontal translation.Use the cursor keys
( to change the value of B again. As you change B notice the
xcoordinate of the
vertex.
** If B=3 where is the vertex? How about B=5? And when B=2?
Make a hypothesis about the relationship between B and the vertex of the
parabola . Test your hypothesis
by entering B=1, B=3, B=5, B=1, and
B=2. Were you correct?
In vertex form Y = A(X  B)^{2} + C, the value of B gives the xcoordinate
of the vertex. Be careful, though.
Notice the form has XB. If you had
the equation Y =(X3)^{2} then B=3 and the vertex is at x = 3. For the
equation Y=(X+1)^{2} the B would be 1 with the vertex at x = 1. 
Studying the Effect of C
1. Press to highlight the C=. Press the
several times and notice the
change in
the graph. Press
several times and notice this change. 

2. Predict where the vertex of the function will
be if you let C=2. Enter 2 for C and
check you prediction. 

3. Make some conclusions about the
effect of changes in C on the vertex. Check your conclusions by
entering
test values for C. 
Studying The Effect of A
1. Return to the Transformation Graphing Screen and press
until the A=
is
highlighted. 

2. Use the same discovery method you
used with B and C to investigate the effect of A on the graph of
the
parabola. Be sure to let A be both negative and positive . Continue with
the next question once you
have a hypothesis, and have checked it, for
the effect of A
** What effect does changing the value of A have on the graph? Be sure
to discuss both magnitude and
sign changes . 
Quick and short check…..
** What is the equation of the parabola (quadratic function) graphed to
the
right? (Note: The scale is 1) 

** Graph the equation y = 3(x +1)^{2} 5
by hand. Check your answer with your calculator. 
You might want to deactivate Interactive Graphing
before continuing.
1. Press [APPS], select the number preceding Interact 

2. Select 1:Uninstall 

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