Quadratic functions in vertex form help

In the movie, Apollo 13, starring Tom Hanks, scenes were filmed involving weightlessness. Weightlessness can be simulated using a plane to fly a special manoeuvre. The plane follows a specific inverted parabolic arc followed by an upward facing recovery arc. Suppose the parabolic arc starts when the plane is at 7200 m and takes it up to 10000 m and then back down to 7200 m again. It covers approximately 16000 m of horizontal distance in total.

Determine the quadratic function that represents the shape of the parabolic path followed by the plane if the origin is at ground level directly below where the plane starts the parabolic arc.

I know I have to use f(x) = a(x-p)^2 + q

Where p = 10000

But after that I don't know what to do. HELP!!!

Re: Quadratic functions in vertex form help

Unfortunately, the one thing you say you know is wrong. The plane will describe a parabolic arc, of the form $\displaystyle y= (x- p)^2+ q$, only if you are taking the y-axis vertically and the x-axis horizontally. The "10000 m" figure is the **height** of the airplane and so is a **y** value, not x.