This problem is much easier than I first thought. The give away is that the 2 parabolas must also intersect y=x!

Therefore, set x = x^{2}+2x-2 which has roots at x = -2 and x = 1. Since the required intersection is in the 1st quadrant, choose x=1

Then y must also be equal to 1; therefore the other parabola must be

7=A(1-16+64) => A = 1/7

Now just to be sure you have it, use your graphing calculator to plot these two parabolas on the same graph!