Answer
The correct graph is $D$.
Work Step by Step
The given function is
$\Rightarrow y=x^2+6x+3$
Add $6$ to each side.
$\Rightarrow y+6=x^2+6x+3+6$
Simplify.
$\Rightarrow y+6=x^2+6x+9$
Write the right side as the square of a binomial.
$\Rightarrow y+6=(x+3)^2$
Write in vertex form.
$\Rightarrow y=(x+3)^2-6$
The vertex is $(-3,-6)$. Because $a$ is positive $(a=1)$, the parabola opens up.
Hence, the correct graph is $D$.
