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