A laboratory designed a radio telescope with a diameter of 300 feet and a maximum depth of 40 feet. The points on a graph are: (-150,40), (150,40). How would I find the equation of this parabola?


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Oddman answered
The curve of the cross section is of the form
  y = ax^2

Put in one of the given values and solve for "a".
  40 = a(150^2)
  40/150^2 = a
  40/22500 = a = 1/5625

The curve is
  y = (x^2)/5625

The depth is given as 40', and the y value 150' from the origin is 40. We assume, then, that the origin is the vertex of the curve. Thus, y = a(x-h)^2 + k reduces to y = ax^2, as (h, k) = (0, 0).

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