Answer
$(2,-16)$
Work Step by Step
The standard form of the equation $
f(x)=x^2-4x-12
$ is
\begin{array}{l}
f(x)=(x^2-4x)-12
\\\\
f(x)=(x^2-4x+4)-12-4
\\\\
f(x)=(x-2)^2-16
.\end{array}
Hence, the vertex is $
(2,-16)
$.
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