select all of the following functions that are quadratic.

$ y = 2x^2 $
$ 3 = 2x^2 - 8 $
$ y = -2 + 2x - 8 $
$ y + 3x = 2x^2 - 8 $
$ y + 3x^2 = 2x + 3x^2 - 8 $

Question

select all of the following functions that are quadratic.

$ y = 2x^2 $
  $ 3 = 2x^2 - 8 $
  $ y = -2 + 2x - 8 $
  $ y + 3x = 2x^2 - 8 $
  $ y + 3x^2 = 2x + 3x^2 - 8 $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Quadratic Functions", "Identifying Quadratic Functions" ], "current_concepts": [ "Quadratic Functions", "Identifying Quadratic Functions" ] } ## Define quadratic function criteria $$ y = ax^2 + bx + c \quad (a e 0) $$ ## Analyze each given equation $$ \begin{aligned} &\text{Option 1: } y = 2x^2 \implies \text{Quadratic (degree 2 in } x\text{)} \ &\text{Option 2: } 3 = 2x^2 - 8 \implies \text{Equation, not a function of } x \text{ and } y \ &\text{Option 3: } y = -2 + 2x - 8 \implies y = 2x - 10 \implies \text{Linear (degree 1)} \ &\text{Option 4: } y + 3x = 2x^2 - 8 \implies y = 2x^2 - 3x - 8 \implies \text{Quadratic (degree 2)} \ &\text{Option 5: } y + 3x^2 = 2x + 3x^2 - 8 \implies y = 2x - 8 \implies \text{Linear (degree 1)} \end{aligned} $$ ## Select the quadratic functions $$ \text{Quadratic functions: } y = 2x^2 \text{ and } y + 3x = 2x^2 - 8 $$

$$y = 2x^2$$

$$3 = 2x^2 - 8$$

$$y = -2 + 2x - 8$$

$$y + 3x = 2x^2 - 8$$

$$y + 3x^2 = 2x + 3x^2 - 8$$

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

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QUESTION IMAGE

Question

Explanation:

Define quadratic function criteria

Analyze each given equation

Select the quadratic functions

Answer: