Function $f$, given by $f(x) = (x+1)(x-3)$, is written in factored form. Recall that this form is helpful for finding the zeros of the function (where the function has the value 0) and for telling us the $x$-intercepts on the graph that represents the function.

Because the inputs -1 and 3 produce an output of 0, they are the zeros of function $f$. And because both $x$ values have 0 for their $y$ value, they also give us the $x$-intercepts of the graph (the points where the graph crosses the $x$-axis, which always have a $y$-coordinate of 0). So, the zeros of a function have the same values as the $x$-coordinates of the $x$-intercepts of the graph of the function.

The factored form can also help us identify the vertex of the graph, which is the point where the function reaches its minimum value. Notice that due to the symmetry of the parabola, the $x$-coordinate of the vertex is 1, and that 1 is halfway between -1 and 3. Once we know the $x$-coordinate of the vertex, we can find its $y$-coordinate by evaluating the function: $f(1) = (1+1)(1-3) = 2 (\text-2) = \text-4$. So the vertex is at $(1,\text-4)$.

When a quadratic function is in standard form, the $y$-intercept is clear: its $y$-coordinate is the constant term $c$ in $ax^2 +bx+c$. To find the $y$-intercept from factored form, we can evaluate the function at $x =0$, because the $y$-intercept is the point at which the graph has an input value of 0. $f(0) = (0+1)(0-3) = (1)(\text-3) = \text-3$.