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Math·Advanced Math·Nonlinear functions

hard

The function $g$ is defined by $g(x)=-2x(x+4)(x-k{)}^2+r$, where $k$ and $r$ are integer constants. In the $xy$-plane, the graph of $y=g(x)$ passes through the point $(6,16)$ and $g(0)=16$. What is the value of $r+k$?

A

$-6$

B

$0$

C

$16$

D

$22$