Parabola and Liner equation

Question

Parabola 1 has the equation y=x^2+2x-2. Parabola 2 has the equation y+6=A(x-8)^2. Find the value of A, such that the two parabolas intersect at a point (r,r) in the same first quadrant.

Answer 1

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 = x²+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!