1. which of the following is a quadratic function?

$ f(x) = 0x^2 + 3x - 6 $

$ f(x) = 2x + 5 $

$ f(x) = 3 - 4x^2 $

$ f(x) = 2^x $

Question

1. which of the following is a quadratic function?

$ f(x) = 0x^2 + 3x - 6 $

$ f(x) = 2x + 5 $

$ f(x) = 3 - 4x^2 $

$ f(x) = 2^x $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Polynomial Classification", "Degree of Polynomial" ], "new_concepts": [ "Quadratic Function Definition" ], "current_concepts": [ "Polynomial Classification", "Degree of Polynomial", "Quadratic Function Definition" ] } ## Define a quadratic function Using the *Polynomial Classification* and *Degree of Polynomial* knowledge points $$ \begin{aligned} &f(x) = ax^2 + bx + c\ &a e 0\ &\text{Degree must be exactly } 2 \end{aligned} $$ ## Analyze the first option Using the *Polynomial Classification* and *Degree of Polynomial* knowledge points $$ \begin{aligned} &f(x) = 0x^2 + 3x - 6 = 3x - 6\ &\text{Degree} = 1 \quad (\text{Linear function}) \end{aligned} $$ ## Analyze the second option Using the *Polynomial Classification* and *Degree of Polynomial* knowledge points $$ \begin{aligned} &f(x) = 2x + 5\ &\text{Degree} = 1 \quad (\text{Linear function}) \end{aligned} $$ ## Analyze the third option Using the *Polynomial Classification* and *Degree of Polynomial* knowledge points $$ \begin{aligned} &f(x) = 3 - 4x^2 = -4x^2 + 3\ &a = -4 e 0\ &\text{Degree} = 2 \quad (\text{Quadratic function}) \end{aligned} $$ ## Analyze the fourth option Using the *Polynomial Classification* and *Degree of Polynomial* knowledge points $$ \begin{aligned} &f(x) = 2^x\ &\text{Variable is in the exponent} \quad (\text{Exponential function}) \end{aligned} $$

(A) $f(x) = 0x^2 + 3x - 6$

(B) $f(x) = 2x + 5$

(C) $f(x) = 3 - 4x^2$

(D) $f(x) = 2^x$

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

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QUESTION IMAGE

Question

Explanation:

Define a quadratic function

Analyze the first option

Analyze the second option

Analyze the third option

Analyze the fourth option

Answer: