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 \(x = - 2\) (by looking at the points where the graph crosses the x - axis).

Step2: Analyze the sign of the function

The graph is a parabola opening downwards (since the coefficient of \(x^{2}\) is negative, as the parabola opens downward). For a downward - opening parabola, the function is negative when \(x < - 6\) or \(x>-2\) (because the graph is below the x - axis (where \(y = f(x)<0\)) for \(x\) values less than the left - most x - intercept and greater than the right - most x - intercept).

Answer:

The domain on which \(f(x)\) is negative is \(x < - 6\) or \(x>-2\) (in interval notation, \((-\infty,-6)\cup(-2,\infty)\))