smc

Question

The parabola with equation p(x) = ax^2+bx+c and vertex (h,k) is reflected about the line y=k. This results in the parabola with equation q(x) = dx^2+ex+f. Which of the following equals a+b+c+d+e+f?

Accepted Answer

We write p(x) as a(x-h)^2+k (this is possible for any parabola). Then the reflection of p(x) is q(x) = -a(x-h)^2+k. Then we find p(x) + q(x) = 2k. Since p(1) = a+b+c and q(1) = d+e+f, we have a+b+c+d+e+f = 2k, so the answer is 2k.