The function f is defined by f(x) = (x + 3)(x + 1). The graph of f in the xy-plane is a parabola. Which
of the following intervals contains the x-coordinate
of the vertex of the graph of f?

Below in bold.

Step-by-step explanation:

The  zeroes ( = x-intercepts) are x = -3 and x = -1.

So the x -coordinate of the vertex is between x = -3 and x = -1.

The actual x-coordinate is halfway between these value: at x = -2.