which function is a quadratic function?

$y - 3x^2 = 3(x^2 + 5) + 1$
$y^2 - 7x = 2(x^2 + 6) + 7$
$y - 2x^2 = 6(x^3 + 5) - 4$
$y - 5x = 4(x + 5) + 9$

Question

which function is a quadratic function?

$y - 3x^2 = 3(x^2 + 5) + 1$
$y^2 - 7x = 2(x^2 + 6) + 7$
$y - 2x^2 = 6(x^3 + 5) - 4$
$y - 5x = 4(x + 5) + 9$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Identifying Quadratic Functions" ], "new_concepts": [], "current_concepts": [ "Identifying Quadratic Functions", "Quadratic Functions" ] } ## Analyze the first option $$ \begin{aligned} y - 3x^2 &= 3(x^2 + 5) + 1 \ y - 3x^2 &= 3x^2 + 15 + 1 \ y &= 6x^2 + 16 \end{aligned} $$ ## Analyze the remaining options $$ \begin{aligned} &\text{Option 2: } y^2 - 7x = 2(x^2 + 6) + 7 \implies y = \pm\sqrt{2x^2 + 7x + 19} \quad (\text{Not a function of form } y = ax^2+bx+c) \ &\text{Option 3: } y - 2x^2 = 6(x^3 + 5) - 4 \implies y = 6x^3 + 2x^2 + 26 \quad (\text{Cubic function}) \ &\text{Option 4: } y - 5x = 4(x + 5) + 9 \implies y = 9x + 29 \quad (\text{Linear function}) \end{aligned} $$ ## Identify the quadratic function $$ y = 6x^2 + 16 \quad (\text{Degree 2 polynomial function of } x) $$

(A) $y - 3x^2 = 3(x^2 + 5) + 1$

(B) $y^2 - 7x = 2(x^2 + 6) + 7$

(C) $y - 2x^2 = 6(x^3 + 5) - 4$

(D) $y - 5x = 4(x + 5) + 9$

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

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QUESTION IMAGE

Question

Explanation:

Analyze the first option

Analyze the remaining options

Identify the quadratic function

Answer: