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Question 1009400: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground and reaches an altitude of 500 feet. If the origin represents the tee and is the ball travels along a parabolic path over the positive x-axis, find an equation for the path of the golf ball.
If the equation that fits this is:
(x-h)^2 = 4x(y-k)
What are
h =
k =
c =
Thank you
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! A simple sketch and reference to STANDARD FORM instead of the format that you show, will allow you to identify the vertex, a maximum point, and the zeros of the equation. You can then find the factor "a", again in reference to  .
Assuming that discussion makes sense for you,
 .
Vertex is (100, 500).
Zeros are x at 0 and at 200.
What about the factor a ?
Use coordinates of either of the zeros....
or simpler
-
The resulting STANDARD FORM equation is  .
The factor of 4 shown in the model you give, does not seem correct. In fact, the factor shown there, "4x", does not fit a quadratic equation, nor parabola.
ANSWERS FROM THIS:
h=100
k=500
What is c supposed to be? What is this supposed to mean?
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If you meant to write the form,  , this is the typical result when deriving the equation of a parabola using a given vertex (h,k) and directrix p units from the vertex and focus p units from the vertex but on the other side from the vertex. If your book does not have this derivation, then you can find a video showing it: vertex of parabola not at origin - derivation of equation using focus and directrix
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