The function $g$ is defined by $g(x) = -2x(x + 4)(x - k)^2 + r$, wher…

Question

Prompt

The function

g

is defined by

g (x) = - 2 x (x + 4) (x - k)^{2} + r

, where

k

and

r

are integer constants. In the

x y

-plane, the graph of

y = g (x)

passes through the point

(6, 16)

and

g (0) = 16

. What is the value of

r + k