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Consider the parabola to our left . It opens up.
All parabolas with a positive leading coefficient
open upwards. The leading coefficient is the
number in front of x2. In the case to our left it is
positive 1. Notice also that the vertex is the
point with the smallest y value on the graph of
the parabola . Mathematically we say it is the
point with the Minimum y value.
Before we start you should set your calculator
to standard zoom by pressing:
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Now we will enter the equation. We will use the
equation
shown in the calculator. Press 
(arrow A). Use the
clear button to remove any equations already present. Use
the up and down arrow to place the curser to the right of the
 = sign. Enter the equation using the
 button
(arrow B) for X. Use the  button for
the square
exponent and use the subtraction symbol on the right
of the calculator (arrow C) for the -6X since we are
subtracting from X2. The key sequence should look like this :
Now press the graph key (arrow D) to graph the
parabola
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Your screen should look like the one at our
right. Now
press  (arrow E) then
 (arrow F)
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Since our parabola is opening upward we want to
find
the x,y pair with the smallest (minimum ) y value. So
chose 3 by pressing  .
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First note the x=0 and y=13 at the bottom of the
screen. This is the coordinate the curser is at. You
can’t see it because at standard zoom the screen
shows from -10 to +10 on both the x and y axis. Since
the curser’s y coordinate is 13 the curser is above the
top of the screen. Notice the Left Bound? Above the
x=0. The calculator is asking for a left limit on the
area it will search for a minimum. The left bound
must be to the left of the vertex but not too far away.
The left and right arrow keys move the curser
along
the graph of the equation shown at the top of the
screen. The up and down arrow keys would jump the
curser to another curve if a second or more equation
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Use the right arrow (arrow g) to move the curser
to
about the same place shown in the picture at left. Notice
the curser is to the left of the vertex marked with the red
circle. (I added this red circle, it will not appear on your
screen) This is a good left bound. Press
 to
accept this left bound.
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Notice the question at the bottom of the screen
has
changed to asking for a right bound. Use the right
arrow to move the curser to the position shown at left.
Notice that this curser is located to the right of the
vertex marked with the red circle. This is a good right
bound. Press
to accept this right bound.
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Notice the two opposing arrows on the screen at
arrow h.
The calculator will search x values between the two arrows
for the minimum y value. If the vertex is not between
these two arrow is will not find it. Notice the question at
the bottom of the screen is asking for a guess. The guess is
the point the calculator will start at searching for the
vertex. Use the left arrow (arrow I) to move the curser
back to the vertex as shown at left. The curser at left is a
good guess. Press
to accept this guess.
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Notice there is Minimum displayed in the bottom
left of the screen and x=2.99999999 y=4. I would
interpret the x=2.9999999 to be x=3
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We need to look at a parabola opening downward.
Press  and
 to remove the first
equation. Enter the equation at left. Notice the
negative in front of X2 is the key at arrow J. Use this
key when there is nothing to subtract from. Use the
minus at arrow K in front of the 5 since it is being
subtracted from 6X. Once the equation is in press .
 Your screen should look like the one
be low : Notice
the
parabola is opening downward. The vertex is not the
smallest y value but the largest. We need to find the
largest y value on the graph of the equation. In
mathematics this is called the maximum y value.
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Press  . You
should see the screen
at the left. Press  to chose the
maximum
function.
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Notice the question is what is the left bound and
the
curser is at x=0, y=-5.
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Use the right arrow (arrow K) to move the curser
to
the point shown at left. This position is relatively
close but definitely to the left of the vertex marked
with the red circle. This makes it a good left bound so
press to
accept this left bound.
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Notice the question has changed to Right Bound?
Asking for a right bound of the area to be searched for
the maximum.
Use the right arrow (arrow L) to move the curser to the
point shown at left. Notice this point is relatively
close to the vertex marked with the red circle but
definitely to the right of the vertex. This makes it an
appropriate right bound. Press
to accept the
right bound.
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Notice the two arrows at arrow M. The calculator
will
search for the maximum between these two arrows. If
the vertex is not between these two arrows it will not
find it. Notice the question in the bottom left of the
screen has changed to Guess? Move the curser left to
the point shown using the left arrow (arrow N). Notice
the guess is as close to the vertex marked with the red
circle as possible. Press
to accept this guess.
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The vertex’ x coordinate is located at
x=2.9999978
(this is an approximation and you must use your
judgment to decide whether or not to round this to
3) The vertex’ y coordinate is at y=4. Remember if
the parabola opens up use the minimum function and
if it opens down use the maximum function.
To graph parabola’s it is useful to find the x intercepts .
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