AMC 12 2009a Problem 9

Suppose that $f(x+3)=3x^2 + 7x + 4$ and $f(x)=ax^2 + bx + c$. What is $a+b+c$?

\textbf{(A)}\ -1 \textbf{(B)}\ 0 \textbf{(C)}\ 1 \textbf{(D)}\ 2 \textbf{(E)}\ 3