Question

Find the vertex of this parabola:
y = -4x2 + 8x - 13

Answer 1

Below in bold.

Explanation:

y = -4x2 + 8x - 13

Divide first 2 terms by -4:-

y = -4(x^2 - 2x) - 13

Convert to vertex form by completing the square:

y = -4[(x - 1)^2 - 1] - 13

y = -4(x - 1)^2 + 4 - 13

y = -4(x - 1)^2 - 9 <---------- Vertex form

y = a(x - j)^2 + k <---------- General form with vertex = (j, k).

So comparing, we see that the vertex is (1, -9).