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