question 10 of 10

which of the equations below could be the equation of this parabola?

a. $y = -2x^2$
b. $x = 2y^2$
c. $y = 2x^2$
d. $x = -2y^2$

Question

question 10 of 10

which of the equations below could be the equation of this parabola?

a. $y = -2x^2$
b. $x = 2y^2$
c. $y = 2x^2$
d. $x = -2y^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Parabola Orientation", "Parabola Vertex" ], "new_concepts": [], "current_concepts": [ "Parabola Orientation", "Parabola Vertex" ] } ## Identify the vertex and orientation of the parabola $$ \begin{aligned} &\text{Vertex: } (h, k) = (0, 0)\ &\text{Orientation: Opens downwards along the } y\text{-axis} \end{aligned} $$ ## Determine the standard equation form $$ \begin{aligned} &y = ax^2\ &a < 0 \end{aligned} $$ ## Match with the given options $$ \begin{aligned} &\text{A. } y = -2x^2 \quad (a = -2 < 0) \quad \checkmark\ &\text{B. } x = 2y^2 \quad (\text{opens right}) \quad \times\ &\text{C. } y = 2x^2 \quad (a = 2 > 0, \text{ opens up}) \quad \times\ &\text{D. } x = -2y^2 \quad (\text{opens left}) \quad \times \end{aligned} $$

A. $y = -2x^2$

B. $x = 2y^2$

C. $y = 2x^2$

D. $x = -2y^2$

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QUESTION IMAGE

Question

Explanation:

Identify the vertex and orientation of the parabola

Determine the standard equation form

Match with the given options

Answer: