Question

Identify the vertex for the graph of y = -2x^2 - 12x + 1.

Answer 1

\[y = -2x^2 - 12x + 1 \\
y = -(2x^2 + 12x - 1) \\
y = -2(x^2 + 6x - \frac 12) \\
y = -2(x^2 + 6x +9 - 9 - \frac 12) \\
y = -2((x+3)^2 - 9 - \frac 12) \\
y = -2((x+3)^2 - \frac {19}{2} ) \\
y = -2(x+3)^2 + 19) \\
\]Compare it to the vertex form of the parabola \(y = a(x-h)^2 + k\) where (h,k) is the vertex. h = -3, k = 19. Vertex is (-3, 19).