#### Answer

$C$

#### Work Step by Step

RECALL:
(1) The vertex form of a quadratic function is $f(x)=a(x-h)^2+k$ where $(h, k)$ are the coordinates of its vertex.
(2) The graph of the quadratic function $f(x) = a(x-h)^2+k$ opens (a) upward when $a \gt 0$, (b) downward when $a \lt0$.
The equation $y=(x+4)^2+2$ can be written as $y=[x-(-4)]^2+2$.
With $a=1$, then the graph of the function is a parabola that opens downward.
This equation is in vertex form with its vertex at $(-4, 2)$.
Therefore, the answer is Option C.