Question

I really need help with this problem...can anyone help me out?

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?

The equation is y=

what is the formula used to answer this?

Answer 1

uese equation of parabola in vertex form, where (h,k) is the vertex:
y=a(x-h)^2 +k
like you know, parabola is symetric repect y axis graph, so since (-160,46),(160,46) are on the parabola, and also noticing that they are symetric respect to y axis, the vertex will be in the middle point between x=-160 and x=160. So at x=0. You also know the maximum depth is 46, it means y=0 is the vertex.
so put this into the equation: y =a(x-0)^2 + 0 =>y=ax^2
now you need to find a. For that substitute the x, y values of one of the points you know they are on parabola: 46=a*160^2 => a=46/160^2
so y=(46/^160^2) x^2 should be the equation