Work Step by Step
If the x-intercepts of a graph are $a,b$, then the function has the form $f(x)=k(x-a)(x-b)$. The x-intercepts are -3, 2, hence the quadratic function becomes $f(x)=k(x+3)(x-2)$. The point (3,12) is on the graph, hence if we plug in the values we get $12=k(6)(1)$. k=2, hence $f(x)=2(x+3)(x-2)$.