Here's the solution.

The vertex lies on Oy, let the vertex of the parabola be (0, y0). The axis is parallel to Ox, this gives a parabola of the form (y - y0)^2 = 4ax

As it passes through (2,2) and (8,-1)

(2 - y0)^2 = 8a and (-1 - y0)^2 = 32a

=> (-1 - y0)^2 = 4*(2 - y0)^2

=> (-1 - y0 - 4 + 2y0)(-1 - y0 + 4 - 2y0) = 0

=> y0 = 5 and y0 = 1

a = (2 - 5)^2 / 8 = 9/8 and a = 1/8

**The required parabola can have two equations:**

**(y - 5)^2 = 9x/2 and (y - 1)^2 = x/2**