Question

What is the vertex of (x) = –16x² + 64x + 80.

Answer 1

(2, 124)

Explanation:

f(x) = a(x - h)² + k - the vertex form of the equation of the parabola with vertex (h, k)

`f(x) = -16x^2+ 64x + 80\\\\f(x) = -16(x^2- 4x) + 80\\\\f(x) = -16(\underline {x^2-2\cdot2x\cdot2+2^2}-2^2) + 80\\\\f(x) = -16\big[(x-2)^2-4\big] + 80\\\\f(x) = -16(x-2)^2+64 + 80\\\\\bold{f(x)=-16(x-2)^2+124\quad\implies\quad h=2\,,\quad k=124}`

The vertex is (2, 124)