Question

What is the axis of symmetry for f(x) = 2x2 + 8x + 8?

Answer 1

http://www.wolframalpha.com/input/?i=axis+of+symmetry+for+f%28x%29+%3D+2x^2+%2B+8x+%2B+8+
\
from the sketch it looks like
x=-2
;)

Answer 2

If you want the answer analytically, then take the first derivative, set it to zero and find the solution(s).

\(\sf f(x) = 2x^2 + 8x + 8\)

\(\sf f('x) = 4x + 8=0\rightarrow x=\dfrac{-8}{4}=-2\)

This gives you the x coordinate of the point on the parabola where a tangent to it has the slope =0. This is where the vertex is and where it would divide the parabola in half (vertically).