identify the graph of $f(x)=-(x - 3)(x + 1)$.

Explanation:

Step1: Find the x - intercepts

Set $f(x)=0$, then $-(x - 3)(x + 1)=0$. So $x-3 = 0$ or $x + 1=0$, which gives $x=3$ and $x=-1$.

Step2: Determine the shape of the parabola

The function $f(x)=-(x - 3)(x + 1)=-x^{2}+2x + 3$ is a quadratic function. The coefficient of $x^{2}$ is $-1<0$, so the parabola opens down - ward.

Step3: Find the vertex

The x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is $x=-\frac{b}{2a}$. For $y=-x^{2}+2x + 3$, $a=-1$, $b = 2$, so $x=-\frac{2}{2\times(-1)} = 1$. Substitute $x = 1$ into $y=-x^{2}+2x + 3$, we get $y=-1 + 2+3=4$. The vertex is $(1,4)$.

The graph with x - intercepts at $x=-1$ and $x = 3$, opening downward and vertex at $(1,4)$ is the correct one.

Answer:

The graph with x - intercepts at $x=-1$ and $x = 3$, opening downward and vertex at $(1,4)$ (you need to visually pick the correct graph from the given options based on these characteristics).