What is the factored form of function f shown in the graph?

The graph shows a parabola with x-intercepts at (-1, 0) and (3, 0). The factored form of a quadratic function is $f(x) = a(x-r_1)(x-r_2)$, where $r_1$ and $r_2$ are the roots. Thus, $f(x) = a(x-(-1))(x-3) = a(x+1)(x-3)$. The vertex is at (1, -4). Substituting this point: $-4 = a(1+1)(1-3) = a(2)(-2) = -4a$. Solving for a gives $a=1$. Therefore, $f(x) = (x+1)(x-3)$.