Question

source
image created for vva via desmos; 2024
(0,2)
(0,1)
(1,0)
(2,0)

Explanation:

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

<reasoning>

Identify the vertex of the parabola from the graph

\[
(h, k) = (1, 0)
\]

Match the vertex coordinates with the given options

\[
(1, 0)
\]
</reasoning>

<answer>
<mcq-option>(A) (0,2)</mcq-option>
<mcq-option>(B) (0,1)</mcq-option>
<mcq-correct>(C) (1,0)</mcq-correct>
<mcq-option>(D) (2,0)</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",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Vertex of Parabola"
],
"new_concepts": [],
"current_concepts": [
"Quadratic Functions",
"Vertex of Parabola"
]
}
</pre_analysis>

<reasoning>

Identify the vertex of the parabola from the graph

\[
(h, k) = (1, 0)
\]

Match the vertex coordinates with the given options

\[
(1, 0)
\]
</reasoning>

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

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