Formula of parabola from two points and the $y$ coordinate of the vertex The parabola has a vertical axis of symmetry. Given two points and the $y$ coordinate of the vertex, how to determine its formula?
For example:


We are dealing with $P=\left\{ \langle x,y\rangle\mid y=q-a\left(x-p\right)^{2}\right\} $
where $(p,q)$ is the vertex. 
Here $q$ is known and the two points belonging to $P$ are giving us two equations in $a$ and $p$.
