If you put the left hand corner at the origin, then you have three points, namely the two x intercepts (0, 0) and (20, 0), and the turning point (10, 10).
The turning point form of the equation will be the easiest to use, . You have (h, k) = (10, 10) and after substituting these and another point as (x, y) you can get the value of a.
Once you have the equation of your curve, set y = 2 and solve for x.