Question

which of the following points represents the vertex of the parabola 1?

a. (-3, 0)
b. (3, 0)
c. (0, -3)
d. (0, 3)

Explanation:

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

<reasoning>

Identify the vertex from the graph

Using the Vertex of Quadratic Function knowledge point, we locate the lowest point (the vertex) of the given parabola 1 on the coordinate plane. Looking at the graph, the curve reaches its minimum point on the y-axis. This point is located at \(x = 0\) and \(y = -3\). Therefore, the coordinates of the vertex of parabola 1 are \((0, -3)\).

Match with the given options

We compare the identified vertex coordinates \((0, -3)\) with the multiple-choice options:

• Option a: \((-3, 0)\)
• Option b: \((3, 0)\)
• Option c: \((0, -3)\)
• Option d: \((0, 3)\)

The correct option is c.
</reasoning>

<answer>
<mcq-option>a. (-3, 0)</mcq-option>
<mcq-option>b. (3, 0)</mcq-option>
<mcq-correct>c. (0, -3)</mcq-correct>
<mcq-option>d. (0, 3)</mcq-option>
</answer>

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

Answer:

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

<reasoning>

Identify the vertex from the graph

Using the Vertex of Quadratic Function knowledge point, we locate the lowest point (the vertex) of the given parabola 1 on the coordinate plane. Looking at the graph, the curve reaches its minimum point on the y-axis. This point is located at \(x = 0\) and \(y = -3\). Therefore, the coordinates of the vertex of parabola 1 are \((0, -3)\).

Match with the given options

We compare the identified vertex coordinates \((0, -3)\) with the multiple-choice options:

• Option a: \((-3, 0)\)
• Option b: \((3, 0)\)
• Option c: \((0, -3)\)
• Option d: \((0, 3)\)

The correct option is c.
</reasoning>

<answer>
<mcq-option>a. (-3, 0)</mcq-option>
<mcq-option>b. (3, 0)</mcq-option>
<mcq-correct>c. (0, -3)</mcq-correct>
<mcq-option>d. (0, 3)</mcq-option>
</answer>

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