Question

source
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\\((1,0), (3,0), (2,-1)\\)
\\((1,0), (3,0)\\)
\\((1,0), (3,0), (0,3)\\)
\\((0,3)\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Zeros of Quadratic Functions",
"Vertex of Parabola"
],
"new_concepts": [],
"current_concepts": [
"Zeros of Quadratic Functions",
"Vertex of Parabola",
"Quadratic Functions"
]
}
</pre_analysis>

<reasoning>

Identify the x-intercepts (zeros) of the parabola

The graph crosses the x-axis at the points where \(y = 0\):
\[
(1, 0) \quad \text{and} \quad (3, 0)
\]

Identify the y-intercept of the parabola

The graph crosses the y-axis at the point where \(x = 0\):
\[
(0, 3)
\]

Match with the given multiple-choice options

The third option lists these three key points:
\[
(1, 0), (3, 0), (0, 3)
\]
</reasoning>

<answer>
<mcq-option>(A) \((1,0), (3,0), (2,-1)\)</mcq-option>
<mcq-option>(B) \((1,0), (3,0)\)</mcq-option>
<mcq-correct>(C) \((1,0), (3,0), (0,3)\)</mcq-correct>
<mcq-option>(D) \((0,3)\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Zeros of Quadratic Functions"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Zeros of Quadratic Functions",
"Vertex of Parabola"
],
"new_concepts": [],
"current_concepts": [
"Zeros of Quadratic Functions",
"Vertex of Parabola",
"Quadratic Functions"
]
}
</pre_analysis>

<reasoning>

Identify the x-intercepts (zeros) of the parabola

The graph crosses the x-axis at the points where \(y = 0\):
\[
(1, 0) \quad \text{and} \quad (3, 0)
\]

Identify the y-intercept of the parabola

The graph crosses the y-axis at the point where \(x = 0\):
\[
(0, 3)
\]

Match with the given multiple-choice options

The third option lists these three key points:
\[
(1, 0), (3, 0), (0, 3)
\]
</reasoning>

<answer>
<mcq-option>(A) \((1,0), (3,0), (2,-1)\)</mcq-option>
<mcq-option>(B) \((1,0), (3,0)\)</mcq-option>
<mcq-correct>(C) \((1,0), (3,0), (0,3)\)</mcq-correct>
<mcq-option>(D) \((0,3)\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Zeros of Quadratic Functions"
]
}
</post_analysis>