Answer
$(-5,-8)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the vertex of the given quadratic function, $
f(x)=(x+5)^2-8
,$ convert the function in the form $f(x)=a(x-h)^2+k.$ Once in this form, the vertex is located at $(h,k).$
$\bf{\text{Solution Details:}}$
In the form $f(x)=a(x-h)^2+k,$ the function above is equivalent to
\begin{array}{l}\require{cancel}
f(x)=(x-(-5))^2-8
.\end{array}
In the function above, $h=
-5
$ and $k=
-8
.$ Hence, the vertex is
\begin{array}{l}\require{cancel}
(-5,-8)
.\end{array}
