# The Parabola Investigation

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```					                                                   The Parabola Investigation
Each person should show ALL of his or her work and answer on separate paper. You should complete this assignment
neatly and submit it to me with your homework quiz next time.

For this investigation, I want you to gain some practice in efficiently keeping and effectively organizing your notes. This
will help you recognize patterns and describe them. As you attempt to answer each question, be sure to keep track of all
the equations you try and their results. An equation that doesn’t work in one case may be the key to a question that
comes later.

a. Graph the parabola y  x . Make an accurate sketch of the graph. Be sure to label any important points on
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your graph. In addition to x- and y-intercepts be sure to label the lowest point, which is called the vertex.

b. Find a way to change the equation to make the same parabola open downward. The new parabola should be
congruent to (the same shape and size as) y  x , with the same vertex, except it should open downward so
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that its vertex will be its highest point.

Find a way to change the equation to make the y  x
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c.                                                                              parabola stretch vertically (it will appear narrower).
The new parabola should have the same vertex and orientation (that is, opening up) as y  x .
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Record the equations you tried, along with their results and your observations.

d. Find a way to change the equation to make the y  x parabola compress vertically (it will appear wider).
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Record the equations you tried, their results, and your observations.

e. Find a way to change the equation to make the y  x
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parabola move 5 units down. That is, your new
parabola should look exactly like y  x but with the vertex at (0, –5).
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Record the equations you tried, along with their results. Include a comment on moving the graph up as well as
down.

Find a way to change the equation to make the y  x parabola move 3 units to the right. That is, your new
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f.
parabola should look exactly like y  x , except that the vertex should be at the point (3, 0). If you need an idea
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to get started, consider things of the form y  ( x  h) where you change h.
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Record the equations you tried, along with their results. Comment on how to move the parabola to the left as well
as how to move it to the right.

g. Finally, find a way to change the equation to make the y  x parabola vertically compressed (wider), open
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down, move 6 units up, and move 2 units to the left. Where is the vertex of your new parabola?

Record the equations you tried, their results, and your comments on how each part of the equation affects its
graph.

The Parabola Investigation – Part II
For each equation below, predict (i) the vertex and (ii) the orientation (open up or down?), and (iii) tell whether it is the
same as a vertical stretch or a compression of y  x . (iv) Sketch a quick graph based on your predictions.
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(a) y   x  9            (b) y  x  7              (c) y  3x                                   y  1 x  1     (e) y   x  7   6
2                   2                             2                                          2                       2
(d)       3

y  5 x  2        (g) y  2 x  3  8 (h) 4 y  4 x                                    y  4x  4
2                      2                              2
(f)        2
(i)

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