Question

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\\(f(x) = 0\\)
\\(f(x) = 1\\)
\\(f(x) = 2\\)
\\(f(x) = -1\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Vertex of Parabola",
"Minimum Value of a Graph"
],
"new_concepts": [],
"current_concepts": [
"Vertex of Parabola",
"Minimum Value of a Graph",
"Quadratic Functions"
]
}
</pre_analysis>

<reasoning>

Identify the vertex of the parabola

Using the Vertex of Parabola knowledge point
\[
(h, k) = (0, 0)
\]

Determine the minimum value of the function

Using the Minimum Value of a Graph knowledge point
\[
\text{Minimum value} = f(0) = 0
\]
</reasoning>

<answer>
<mcq-correct>(A) \(f(x) = 0\)</mcq-correct>
<mcq-option>(B) \(f(x) = 1\)</mcq-option>
<mcq-option>(C) \(f(x) = 2\)</mcq-option>
<mcq-option>(D) \(f(x) = -1\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Vertex of Parabola"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Vertex of Parabola",
"Minimum Value of a Graph"
],
"new_concepts": [],
"current_concepts": [
"Vertex of Parabola",
"Minimum Value of a Graph",
"Quadratic Functions"
]
}
</pre_analysis>

<reasoning>

Identify the vertex of the parabola

Using the Vertex of Parabola knowledge point
\[
(h, k) = (0, 0)
\]

Determine the minimum value of the function

Using the Minimum Value of a Graph knowledge point
\[
\text{Minimum value} = f(0) = 0
\]
</reasoning>

<answer>
<mcq-correct>(A) \(f(x) = 0\)</mcq-correct>
<mcq-option>(B) \(f(x) = 1\)</mcq-option>
<mcq-option>(C) \(f(x) = 2\)</mcq-option>
<mcq-option>(D) \(f(x) = -1\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Vertex of Parabola"
]
}
</post_analysis>