Answer:
(-3, -17)
Step-by-step explanation:
The best way to find the vertex is to rewrite the given quadratic in vertex form: y - k = a(x - h)^2.
The given quadratic is f(x) = 2x2 + 12x + 1. We will focus on the first two terms and "complete the square." f(x) = 2x2 + 12x + 1 can be rewritten as
f(x) = 2(x^2 + 6x) + 1, which, after completing the square, is
f(x) = 2(x^2 + 6x + 9 - 9) + 1, or
f(x) = 2( (x + 3)^2 - 9 ) + 1, or
f(x) = 2(x + 3)^2 - 17
Comparing this to
f(x) = a(x - h)^2 + k, we see that the vertex is located at (h, k): (-3, -17)
