Question

what is the decreasing interval for this graph?

Explanation:

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<reasoning>

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 \(x > 1\).
</reasoning>

<answer>
\((1, \infty)\) (or \(x > 1\))
</answer>

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Answer:

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</pre_analysis>

<reasoning>

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 \(x > 1\).
</reasoning>

<answer>
\((1, \infty)\) (or \(x > 1\))
</answer>

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