which function is a quadratic function?

$p(x) = 2x(x^2 + 6) + 1$

$t(x) = -8x^2(x^2 - 6) + 1$

$m(x) = -4(x + 3) - 2$

$h(x) = 3x(x - 2) - 4$

Question

which function is a quadratic function?

$p(x) = 2x(x^2 + 6) + 1$

$t(x) = -8x^2(x^2 - 6) + 1$

$m(x) = -4(x + 3) - 2$

$h(x) = 3x(x - 2) - 4$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Functions", "Polynomial Degree" ], "new_concepts": [], "current_concepts": [ "Quadratic Functions", "Polynomial Degree" ] } ## Define quadratic function criteria $$ f(x) = ax^2 + bx + c, \quad a eq 0 $$ ## Expand and determine degree of each option $$ \begin{aligned} p(x) &= 2x(x^2 + 6) + 1 = 2x^3 + 12x + 1 \quad (\text{Degree } 3) \ t(x) &= -8x^2(x^2 - 6) + 1 = -8x^4 + 48x^2 + 1 \quad (\text{Degree } 4) \ m(x) &= -4(x + 3) - 2 = -4x - 14 \quad (\text{Degree } 1) \ h(x) &= 3x(x - 2) - 4 = 3x^2 - 6x - 4 \quad (\text{Degree } 2) \end{aligned} $$ ## Identify the quadratic function $$ h(x) = 3x^2 - 6x - 4 $$

(A) $p(x) = 2x(x^2 + 6) + 1$

(B) $t(x) = -8x^2(x^2 - 6) + 1$

(C) $m(x) = -4(x + 3) - 2$

(D) $h(x) = 3x(x - 2) - 4$

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

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QUESTION IMAGE

Question

Explanation:

Define quadratic function criteria

Expand and determine degree of each option

Identify the quadratic function

Answer: