Question

A laboratory designed a radio telescope with a diameter of 380 feet and a maximum depth of 42 feet. The graph depicts a cross section of this telescope. Find the equation of this parabola.

Answer 1

We don't get to see the graph, so will assume the simplest equation with vertex at origin.
The equation is
y=ax^2
with x=380/2=190', y=42'
so
42=a(190^2) => a=42/190^2=21/18050

the equation is therefore
y=21x^2/18050
and kept in exact form above for accuracy required for a telescope.

If the graph shows the vertex elsewhere at (h,k), the equation is then
y=21(x-h)^2/18050+k