Question

What is the vertex of the graph of the function f(x) = x^2 + 8x − 2 ?

a (−4, 18)
b (0, -2)
c (-8, -2)
d (−4, −18)

Answer 1

The vertex is at (-4, -18) (Fourth answer choice)

Explanation:

The standard vertex equation of a parabola is f(x) = (x - h)^2 + k.

"Completing the square" is one of the faster and better ways of determining the vertex:

f(x) = x^2 + 8x - 2 => f(x) = x^2 + 8x + 16 - 16 - 2 => (x + 4)^2 - 18. Comparing this to (x - h)^2 + k, we see that h = -4 and k = -18. The vertex is at (-4, -18).