I am writing a computer program that needs to be able to find positions in parabolic arcs.

I need to calculate the position of a projectile after traveling a given distance.
I have $X\_0, Y\_0, X\_1, Y\_1$, and $Y\_{max}$. What is the equation I would use to find $Y$ at a given $X$ value?

Since this is for a computer program, the answer should be in the form of a single equation. It may be assumed that the initial variables are valid.