Question

what is the decreasing interval for this graph?

Explanation:

Identify the vertex of the parabola

The graph shows a parabola opening upwards. The lowest point, or vertex, is located at the coordinates \((1, 0)\).

Determine where the function increases

A function is increasing on an interval if the \(y\)-values increase as the \(x\)-values move from left to right. Looking at the graph, to the right of the vertex \(x = 1\), the curve goes upwards.

Write the interval in standard notation

The graph continues upwards to the right indefinitely. Therefore, the interval where the graph is increasing starts at \(x = 1\) and goes to infinity, written as \((1, \infty)\) or \(x > 1\).

Answer:

\((1, \infty)\) (or \(x > 1\))