Answer the Question $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$

Multiple Choice

Answer the question.
-Determine the function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ so that its graph contains the points $( - 1,2 ) , ( 0,6 ) , ( 1,16 )$ , and $( 2$ , 50) .

A) $f ( x ) = 3 x ^ { 3 } + 3 x ^ { 2 } - 4 x - 6$
B) $f ( x ) = 3 x ^ { 3 } + 3 x ^ { 2 } + 4 x + 6$
C) $f ( x ) = 3 x ^ { 3 } + 4 x ^ { 2 } + 3 x + 6$
D) $f ( x ) = 4 x ^ { 3 } + 4 x ^ { 2 } + 4 x + 6$