Question

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\\(0 < x < 1\\)
\\(-1 < x < \infty\\)
\\(1 < x < \infty\\)
\\(-\infty < x < 1\\)

Explanation:

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"concepts_used": [],
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"current_concepts": [
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"Vertex of Parabola"
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</pre_analysis>

<reasoning>

Identify the vertex of the parabola

The vertex of the parabola is located at the minimum point on the graph, which is \( (1, 0) \).

Determine the interval where the function is increasing

The function increases where the graph rises from left to right. This occurs to the right of the vertex, where \( x > 1 \).

Match with the given options

The interval \( x > 1 \) is represented in inequality notation as \( 1 < x < \infty \).
</reasoning>

<answer>
<mcq-option>(A) \(0 < x < 1\)</mcq-option>
<mcq-option>(B) \(-1 < x < \infty\)</mcq-option>
<mcq-correct>(C) \(1 < x < \infty\)</mcq-correct>
<mcq-option>(D) \(-\infty < x < 1\)</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Increasing Intervals"
]
}
</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Identify the vertex of the parabola

The vertex of the parabola is located at the minimum point on the graph, which is \( (1, 0) \).

Determine the interval where the function is increasing

The function increases where the graph rises from left to right. This occurs to the right of the vertex, where \( x > 1 \).

Match with the given options

The interval \( x > 1 \) is represented in inequality notation as \( 1 < x < \infty \).
</reasoning>

<answer>
<mcq-option>(A) \(0 < x < 1\)</mcq-option>
<mcq-option>(B) \(-1 < x < \infty\)</mcq-option>
<mcq-correct>(C) \(1 < x < \infty\)</mcq-correct>
<mcq-option>(D) \(-\infty < x < 1\)</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Increasing Intervals"
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