Answer
The correct graph is $A$.
Work Step by Step
The given function is
$\Rightarrow y=-x^2+8x-12$
Subtract $4$ from each side.
$\Rightarrow y-4=-x^2+8x-12-4$
Simplify.
$\Rightarrow y-4=-x^2+8x-16$
Factor out $-1$.
$\Rightarrow y-4=-1(x^2-8x+16)$
Write the right side as the square of a binomial.
$\Rightarrow y-4=-1(x-4)^2$
Write in vertex form.
$\Rightarrow y=-1(x-4)^2+4$
The vertex is $(4,4)$. Because $a$ is negative $(a=1)$, the parabola opens down.
Hence, the correct graph is $A$.
