Select the function that represents a parabola with zeros at \( x = - 2 \) and \( x = 4 , \) and \( y \) - intercept \( ( 0 , - 16 ) \) .
A) \( f ( x ) = 2 x ^ { 2 } + 4 x - 16 \)
B) \( f ( x ) = 2 x ^ { 2 } - 4 x - 16 \)
C) \( f ( x ) = x ^ { 2 } - 2 x - 8 \)
D) \( f ( x ) = x ^ { 2 } + 2 x - 8\)