Question

What is the vertex for the graph of y = -2x^2 + 8x - 13?
Answer
(2, 11)
(2, -5)
(-2, -37)
(-2, -21)

Answer 1

I assume by 'vertex' you mean the turning point. By differentiation:
\[\frac{d}{dx} -2x^2 + 8x - 13 = -4x + 8\]
The derivative is 0 at turning points, so we get the equation
\[ -4x + 8 = 0 \\
-4x = -8\\
x = 2 \]