Question

determine the domain on which the following function is increasing.

Explanation:

Step1: Recall the concept of increasing function

A function \(y = f(x)\) is increasing on an interval if for any two points \(x_1\) and \(x_2\) in that interval with \(x_10\)), it opens upwards. The vertex form of a parabola is \(y=a(x - h)^{2}+k\), and the axis of symmetry is \(x = h\). The function is decreasing to the left of the axis of symmetry and increasing to the right of the axis of symmetry.

Step2: Find the axis of symmetry from the graph

From the graph, we can observe that the axis of symmetry (the \(x\) - coordinate of the vertex) is \(x=- 4\).

Answer:

The function is increasing on the interval \((-4,\infty)\)