The shape of the quadratic function is called a parabola and obeys a very important rule. Say we have a sideways parabola: $$x = f(y) = Ay^2.$$

Imagine rays (show pic!) of light coming from infinity from the right and striking the surface of the parabola. All the rays will be reflected towards the point $F=(\frac{p}{2},0)$ where $p = \frac{1}{2A}$.

( probably need a better drawing.)

You put the receiver in the focus point, and you get all the power incident on the dish concentrated right on your receiver.