Question

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

Explanation:

Step1: Identify x-intercepts

The graph intersects the x - axis at \(x=-4\) and \(x = 0\).

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

The graph of the function is a parabola opening downwards (since the coefficient of \(x^{2}\) is negative, as the ends of the parabola go down). For a downward - opening parabola, the function is positive between its two x - intercepts. So, the values of \(x\) for which \(f(x)>0\) are between \(-4\) and \(0\), i.e., \(-4 < x<0\).

Answer:

The domain on which \(f(x)\) is positive is \(-4 < x<0\) (or in interval notation \((-4,0)\))