Question

determine the domain on which the following function is decreasing.

Explanation:

Step1: Identify the vertex of the parabola

The graph is a parabola opening upwards (since the coefficient of \(x^2\) is positive, as seen from the shape). The vertex is the minimum point of the parabola. From the graph, we can observe that the vertex (minimum point) occurs at \(x = 4\) (by looking at the lowest point on the graph, which is at \(x = 4\)).

Step2: Determine the interval where the function is decreasing

For a parabola opening upwards, the function is decreasing to the left of the vertex (where the \(x\)-coordinate of the vertex is \(h\), the function decreases on the interval \((-\infty, h)\)). Here, the vertex is at \(x = 4\), so the function is decreasing when \(x < 4\), or in interval notation, \((-\infty, 4)\).

Answer:

The function is decreasing on the interval \((-\infty, 4)\) (or \(x < 4\)).