Answer
It is a parabola.
See Graph I for the equation.
Work Step by Step
For $y = x^2 + 12x +36$, we can make it into
$y = x^2 + 12x + (\frac{12}{2})^2 + 36 - (\frac{12}{2})^2$
$y = (x + 6)^2,$
which is a parabola that opens upward and with lowest point at $(-6, 0)$. The axis of symmetry is $x = -6$.
See Graph I for the equation.
