#### Answer

$(0,-4)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To find the vertex of the given quadratic function, $
f(x)=x^2-4
,$ 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)^2-4
\\\\
f(x)=(x-0)^2-4
.\end{array}
In the function above, $h=
0
$ and $k=
-4
.$ Hence, the vertex is
\begin{array}{l}\require{cancel}
(0,-4)
.\end{array}