Question

which is the graph of $f(x) = -(x + 3)(x + 1)$?

Explanation:

Step1: Find x-intercepts

Set \( f(x) = 0 \), so \( -(x + 3)(x + 1)=0 \). Then \( x + 3 = 0 \) or \( x + 1 = 0 \), giving \( x=-3 \) and \( x=-1 \). The graph should cross the x - axis at \( x=-3 \) and \( x=-1 \).

Step2: Determine parabola direction

The coefficient of \( x^{2} \) (after expanding) is - 1 (since \( -(x + 3)(x + 1)=-(x^{2}+4x + 3)=-x^{2}-4x - 3 \)). A negative leading coefficient means the parabola opens downward.
Looking at the graphs, the second graph (middle - top) has x - intercepts at \( x=-3 \) and \( x=-1 \) and opens downward.

Answer:

The Middle - Top Graph (the second graph in the top row)