Question

use the graph to find the solutions of this quadratic function.

(x = ?, \quad)

enter the smallest solution first.

Explanation:

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"concepts_used": [
"Coordinate Plane",
"x-intercept"
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"Coordinate Plane",
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</pre_analysis>

<reasoning>

Identify the meaning of solutions on a graph

Using the x-intercept and Coordinate Plane knowledge points
\[
\text{Solutions of } f(x) = 0 \text{ correspond to the } x\text{-intercepts of the graph } y = f(x).
\]

Locate the x-intercepts from the graph

Using the Coordinate Plane knowledge point
\[
\text{The parabola crosses the } x\text{-axis at } x = -3 \text{ and } x = -1.
\]

Order the solutions

The problem requires entering the smallest solution first:
\[
-3 < -1 \implies x = -3, -1
\]
</reasoning>

<answer>
Use the graph to find the solutions of this quadratic function.

\(x =\) <blank>-3</blank>, <blank>-1</blank>

Enter the smallest solution first.
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Graphical Solutions of Quadratics"
]
}
</post_analysis>

Answer:

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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
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"concepts_used": [
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"Coordinate Plane",
"x-intercept",
"Graphical Solutions of Quadratics",
"Quadratic Roots"
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}
</pre_analysis>

<reasoning>

Identify the meaning of solutions on a graph

Using the x-intercept and Coordinate Plane knowledge points
\[
\text{Solutions of } f(x) = 0 \text{ correspond to the } x\text{-intercepts of the graph } y = f(x).
\]

Locate the x-intercepts from the graph

Using the Coordinate Plane knowledge point
\[
\text{The parabola crosses the } x\text{-axis at } x = -3 \text{ and } x = -1.
\]

Order the solutions

The problem requires entering the smallest solution first:
\[
-3 < -1 \implies x = -3, -1
\]
</reasoning>

<answer>
Use the graph to find the solutions of this quadratic function.

\(x =\) <blank>-3</blank>, <blank>-1</blank>

Enter the smallest solution first.
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Graphical Solutions of Quadratics"
]
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</post_analysis>