Question

A laboratory designed a radio telescope with a diameter of 320 feet and a maximum depth of 46 feet. Points on graph are: (-160,46),(160,46). Find the equation of this parabola.

Answer 1

the shape of the telescope is said to be a parabola. In this case, the general form which we will pattern our equation is y- k= 4a(x – h)^2
(h,k) or vertex = (0,0)
y = 4ax^2
We substitute x = 320/2 = 160, y = 46

46 = 4a (160)^2
46 = 4a (25600)
4a = 23/12800
hence the equation is y = (23/12800)x^2