To find the axis of symmetry, one way is to convert the equation to vertex form and you can find the symmetry from the vertex
f(x) = 2(x^2 + 4x + ) + 8 -
f(x) = 2(x^2 + 4x + (4/2)^2 ) + 8 - (4/2)^2
f(x) = 2(x^2 + 4x + 4 ) + 8 - 4
f(x) = 2(x + 2)^2 + 4 - Vertex form
Vertex is (-2, 4) so the axis of symmetry is x = -2