Since parabolas are symmetrical and this one has its minimum at (0,0), we know now what the actual points are at each corner of our square:
And that, friends, is where this gets fun. Let's use (4,8) since both numbers are positive. Now that we have a point on our parabola, we just need to plug values in for x and y!
y = ax2
8 = a(4)2
8 = 16a
0.5 = a
This would, of course, also work with (-4,8). Either way, you're going to get 0.5 (or 1/2) for a.