Question

copy and complete the table of values for (y = 3x^2 + 2)

what numbers replace a and b?

\

$$\begin{array}{c||c|c|c|c|c} x & -3 & -2 & -1 & 0 & 1 \\\\ \\hline y & 29 & a & 5 & b & 5 \\end{array}$$

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Quadratic Evaluation",
"Table of Values"
],
"current_concepts": [
"Quadratic Evaluation",
"Table of Values"
]
}
</pre_analysis>

<reasoning>

Evaluate the function at x = -2

\[

$$\begin{aligned} y &= 3(-2)^2 + 2 \\ &= 3(4) + 2 \\ &= 14 \end{aligned}$$

\]

Evaluate the function at x = 0

\[

$$\begin{aligned} y &= 3(0)^2 + 2 \\ &= 0 + 2 \\ &= 2 \end{aligned}$$

\]
</reasoning>

<answer>

\(x\)	\(-3\)	\(-2\)	\(-1\)	\(0\)	\(1\)

\(A = 14\), \(B = 2\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Evaluation"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Quadratic Evaluation",
"Table of Values"
],
"current_concepts": [
"Quadratic Evaluation",
"Table of Values"
]
}
</pre_analysis>

<reasoning>

Evaluate the function at x = -2

\[

$$\begin{aligned} y &= 3(-2)^2 + 2 \\ &= 3(4) + 2 \\ &= 14 \end{aligned}$$

\]

Evaluate the function at x = 0

\[

$$\begin{aligned} y &= 3(0)^2 + 2 \\ &= 0 + 2 \\ &= 2 \end{aligned}$$

\]
</reasoning>

<answer>

\(x\)	\(-3\)	\(-2\)	\(-1\)	\(0\)	\(1\)

\(A = 14\), \(B = 2\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Evaluation"
]
}
</post_analysis>