Answer
$(-4,-9)$
Work Step by Step
The standard form of the given quadratic function, $f(x)=
x^2+8x+7
,$ is
\begin{array}{l}\require{cancel}
f(x)=\left( x^2+8x \right)+7
\\\\
f(x)=\left( x^2+8x+\left( \dfrac{8}{2} \right)^2 \right)+7-\left( \dfrac{8}{2} \right)^2
\\\\
f(x)=\left( x^2+8x+16 \right)+7-16
\\\\
f(x)=\left( x+4 \right)^2-9
.\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,-9)
.\end{array}
