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 $( - 1 , - 9 ) , ( 0 , - 3 ) , ( 1,7 )$ , and $( 2,33 )$ .

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