Question

determine the domain on which the following function is increasing.

Explanation:

Step1: Analyze the graph of quadratic function

For a parabola \(y = ax^{2}+bx + c\) (\(a
eq0\)), if \(a>0\), it opens upwards. The vertex of the parabola is the minimum - point. The function is decreasing on the left - hand side of the vertex and increasing on the right - hand side of the vertex.
From the graph, we can observe that it is a parabola opening upwards (since the coefficient of \(x^{2}\) is positive).

Step2: Locate the vertex \(x\) - coordinate

The vertex of a parabola \(y = ax^{2}+bx + c\) has the \(x\) - coordinate \(x=-\frac{b}{2a}\). From the graph, we can see that the vertex of the parabola has an \(x\) - value. By visual inspection (counting the grid points), we find that the vertex of the parabola occurs at \(x = 2\).

Answer:

The function is increasing on the interval \((2,\infty)\)