Question

the graph of $y = f(x)$ is shown below. find all values of $x$ for which $f(x) < 0$.

Explanation:

Step1: Identify x-intercepts

The graph intersects the x - axis at \(x=-5\) and \(x = 3\).

Step2: Determine where \(f(x)<0\)

For a parabola opening upwards (since the coefficient of \(x^{2}\) is positive, as the parabola opens up), the function \(f(x)\) is less than 0 (below the x - axis) between its two x - intercepts. So we look for the interval of \(x\) values between \(x=-5\) and \(x = 3\).

Answer:

\(-5 < x < 3\)