Model a parabolic mirror, using the function y=x^2/8.

Create a tangent to the curve, and a vertical line going through the tangency point.  Reflect the vertical ray in the tangent line:

Inspect the equation of the reflected ray and observe that the y intercept remains the same as you drag the point A along the curve:

What happens if you steepen or flatten the mirror by changing the coefficient of x^2?

Can you come up with a formula for the y intercept as a function of the coefficient of x^2?