Locate the point on the curve with the smallest $y$-value (the bottom of the U-shape).

The question asks for the minimum value of the function, which is the $y$-coordinate of that lowest point.

From the graph, the $x$-intercepts are at $x=-3$ and $x=1$. In Desmos, enter $y=a(x+3)(x-1)$.

From the graph, the parabola crosses the $y$-axis at $(0,-3)$. In Desmos, enter the point $(0,-3)$ and adjust the slider $a$ until the graph passes through that point (you should get $a=1$).

With the correct graph shown, click the lowest point (vertex) and read its $y$-coordinate. That $y$-value is the minimum value of $f(x)$.

Because the graph is a U-shaped parabola opening upward, its minimum occurs at the lowest point on the curve (the vertex).

From the graph, the vertex is at $(-1,-4)$, so the minimum value of $f(x)$ is $-4$.