Answer
Vertex: $(-5,106)$
Axis of symmetry: $x=-5$
Work Step by Step
Factor out the coefficient of $x^2$ and square half of the coefficient of the $x$-term: $\left(\frac{1}{2} \cdot 10\right)^2=25$. Adding and subtracting this number after the $x$-term gives
$$
\begin{aligned}
&w(x)=-3 x^2-30 x+31\\
& w(x)=-3\left(x^2+10 x-\frac{31}{3}\right) \\
& w(x)=-3\left(x^2+10 x+25-25-\frac{31}{3}\right) \\
& w(x) = -3\left(x^2+10x+25\right)-3\left(-\frac{106}{3}\right) \\
&w(x)=-3(x+5)^2+106
\end{aligned}
$$
The vertex is $(-5,106)$ and the axis of symmetry is $x=-5$.
