College Algebra & Trigonometry, 2018a

5.3. APPLICATIONS OF THE PARABOLA 281
Here’s what this cross-section looks like:
4
(−4, 3) (4, 3)
3
2
1
−4 −3 −2 −1 1 2 3 4
−1
Taking the standard equation for an upward facing parabola: 4p(y − k) =(x − h) 2
and using the point (0, 0) for the vertex leaves us with 4p(y − 0) = (x − 0) 2 or
4py = x 2 .
The main thing we need to do is find the value of p for this situation. This will
tell us where the receiver should be on the satellite dish. Plugging in the points
on the graph that we know will allow us to solve for p.
4py = x 2
4p(3) = (4) 2
12p =16
p = 4 3
Thus the receiver should be 4 feet or 1 foot 4 inches from the bottom of the dish.
3