How do I find the equation of a parabola given the max, and two points? I was given the points (2, -1) and (10,-1) and also a max of 4.  How would I go about finding the equation of the parabola given this info?

Notice that the $y$ values of those points are equal, which implies they are equidistant from the axis of symmetry.  Therefore the vertex is at $(6,4)$.  Since $x^2$ increases from $0$ to $16$ as $x$ goes from $0$ to $4$, but your parabola decreases by $5$ when you go $4$ units to the right (or left) of the vertex, there must be a scaling factor of $-\frac{5}{16}$.  So I would conclude that $y=-\frac{5}{16}(x-6)^2+4$ is the equation.
