Answer
The function has a maximum value of $-5$.
Work Step by Step
The given function is
$\Rightarrow y=-x^2-10x-30$
Add $5$ to each side.
$\Rightarrow y+5=-x^2-10x-30+5$
Simplify.
$\Rightarrow y+5=-x^2-10x-25$
Factor out $-1$ from the right side.
$\Rightarrow y+5=-1(x^2+10x+25)$
Write the right side as the square of a binomial.
$\Rightarrow y+5=-1(x+5)^2$
Write in vertex form.
$\Rightarrow y=-1(x+5)^2-5$
The vertex is $(-5,-5)$. 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 $-5$.
