Question

determine the domain on which the following function is decreasing.

Explanation:

Step1: Recall the definition of a decreasing function

A function \(y = f(x)\) is decreasing on an interval if for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step2: Analyze the graph

Looking at the given parabola (a quadratic function \(y = ax^{2}+bx + c\) with \(a<0\) since it opens down - ward). The vertex of the parabola is the maximum point. For a parabola \(y = ax^{2}+bx + c\) (\(a<0\)), the function is increasing to the left of the vertex and decreasing to the right of the vertex.
From the graph, the vertex (maximum point) occurs at \(x=-3\).

Answer:

The function is decreasing on the interval \((-3,\infty)\)