Answer
$g(x)=-2(x-3)^2+22$
Vertex: $(3,22)$
Axis of symmetry: $x=3$.
Work Step by Step
Factor out the coefficient of $x^2$ and square of half the coefficient of the $x$-term: $(-6 / 2)^2=9$. Adding and subtracting this number after the $x$-term gives
$$
\begin{aligned}
& g(x)=-2\left(x^2-6 x+9-9-2\right) \\
& g(x)=-2\left((x-3)^2-11\right) \\
& g(x)=-2(x-3)^2+22
\end{aligned}
$$
The vertex is $(3,22)$ and the axis of symmetry is $x=3$.
