Suppose $a , b , c \in \mathbb { R }$ and $$f ( x ) = a x ^ { 2 } + b x + c , x \in \mathbb { R } .$$ If $0 \leq f ( x ) \leq ( x - 1 ) ^ { 2 }$ for all $x$, and $f ( 3 ) = 2$, then
(A) $a = \frac { 1 } { 2 } , b = - 1 , c = \frac { 1 } { 2 }$.
(B) $a = \frac { 1 } { 3 } , b = - \frac { 1 } { 3 } , c = 0$.
(C) $a = \frac { 2 } { 3 } , b = - \frac { 5 } { 3 } , c = 1$.
(D) $a = \frac { 3 } { 4 } , b = - 2 , c = \frac { 5 } { 4 }$.