Question

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

Explanation:

Step1: Find the x - intercepts

Set \(f(x)=(x - 3)(x + 1)=0\). By the zero - product property, \(x-3 = 0\) gives \(x = 3\) and \(x+1=0\) gives \(x=-1\). So the x - intercepts are \(x = 3\) and \(x=-1\).

Step2: Determine the shape of the parabola

The function \(y=(x - 3)(x + 1)=x^{2}-2x - 3\) is a quadratic function with a positive leading coefficient (\(a = 1\) when expanded to the form \(y=ax^{2}+bx + c\)). So the parabola opens upward.

Answer:

The graph of the function \(y=(x - 3)(x + 1)\) is a parabola that opens upward and has x - intercepts at \(x=-1\) and \(x = 3\). Among the given graphs, the one that matches these characteristics is the correct one (you would need to visually inspect the graphs to pick the specific one with x - intercepts at \(-1\) and \(3\) and opening upward).