Equation of a badminton birdie

So the problem goes like this:

In an underhand serve, the birdie starts from a point 2m above the ground and travels a horizontal distance of 20m before it strikes the floor. The birdie travels in a parabolic path and reaches it's highest point after traveling a horizontal distance of 9m. Determine the equation of the parabola in the form $\displaystyle y-k=a(x-h)^2$.

So I know of course that $\displaystyle (x-h)$ becomes $\displaystyle (x-9)$. The vertex is $\displaystyle (9,k)$. $\displaystyle a$ would have to be negative, since the parabola opens downwards.

Any actual solving the equation has me stumped, Conics wasn't my best unit =\