Question

determine the domain on which the following graph of f(x) is negative.

Explanation:

Step1: Identify x-intercepts

The graph intersects the x - axis at \(x=-6\) and \(x = - 2\).

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

The parabola opens upwards (since the coefficient of \(x^{2}\) is positive, as the graph has a minimum point). For a parabola opening upwards, the function is negative between its two x - intercepts. So we need to find the interval of \(x\) values between \(x=-6\) and \(x=-2\).

Answer:

\(-6 < x < -2\) (or in interval notation \((-6,-2)\))