Answer
$(-4,-14)$
Work Step by Step
The standard form of the given quadratic function, $f(x)=
-x^2-8x+2
,$ is
\begin{array}{l}\require{cancel}
f(x)=\left( -x^2-8x \right)+2
\\\\
f(x)=-\left( x^2+8x \right)+2
\\\\
f(x)=-\left( x^2+8x+\left( \dfrac{8}{2} \right)^2 \right)+2-\left( \dfrac{8}{2} \right)^2
\\\\
f(x)=-\left( x^2+8x+16 \right)+2-16
\\\\
f(x)=-\left( x+4 \right)^2-14
.\end{array}
Since the vertex of $f(x)=a(x-h)^2+k$ is at $(h,k)$, then the vertex of the equation above is
\begin{array}{l}\require{cancel}
(-4,-14)
.\end{array}
