SAT Right triangles Question

The function $f$ is defined by $f(x)=a{x}^2+bx+c$ , where $a,b$ , and $c$ are constant, and $1<a<4$ . The graph of $y=f(x)$ in the xy-plane passes through the points (12, 0) (-6, 0). If $a$ is an integer, what could be the value of $a+b$ ?