choose the function that represents the data in the table.

\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
y & 0 & 3 & 12 & 27 & 48 & 75 \\
\hline
\end{array}

$y = x^2$
$y = 3x^2$
$y = x^2 + 3$
$y = 2x + 3$

Question

choose the function that represents the data in the table.

\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
y & 0 & 3 & 12 & 27 & 48 & 75 \\
\hline
\end{array}

$y = x^2$
$y = 3x^2$
$y = x^2 + 3$
$y = 2x + 3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Evaluation" ], "new_concepts": [], "current_concepts": [ "Function Evaluation", "Quadratic Modeling" ] } ## Analyze the data points from the table $$ (x, y) \in \{(0,0), (1,3), (2,12), (3,27), (4,48), (5,75)\} $$ ## Test the given options with the first data points $$ \begin{aligned} &\text{For } y = x^2: \quad x=1 \implies y=1^2=1 e 3 \ &\text{For } y = 3x^2: \quad x=0 \implies y=3(0)^2=0, \quad x=1 \implies y=3(1)^2=3, \quad x=2 \implies y=3(2)^2=12 \ &\text{For } y = x^2 + 3: \quad x=0 \implies y=0^2+3=3 e 0 \ &\text{For } y = 2x + 3: \quad x=0 \implies y=2(0)+3=3 e 0 \end{aligned} $$ ## Verify the matching function for all remaining points $$ \begin{aligned} &x=3 \implies y=3(3)^2=27 \ &x=4 \implies y=3(4)^2=48 \ &x=5 \implies y=3(5)^2=75 \end{aligned} $$

(A) $y = x^2$

(B) $y = 3x^2$

(C) $y = x^2 + 3$

(D) $y = 2x + 3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Modeling" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the data points from the table

Test the given options with the first data points

Verify the matching function for all remaining points

Answer: