question 1 of 10

the vertex of this parabola is at (-2, 1). which of the following could be its equation?

a. (y = 4(x - 2)^2 - 1)

b. (x = 4(y - 1)^2 - 2)

c. (y = 4(x - 2)^2 + 1)

d. (x = 4(y + 1)^2 - 2)

Question

question 1 of 10

the vertex of this parabola is at (-2, 1). which of the following could be its equation?

a. (y = 4(x - 2)^2 - 1)

b. (x = 4(y - 1)^2 - 2)

c. (y = 4(x - 2)^2 + 1)

d. (x = 4(y + 1)^2 - 2)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parabola Orientation", "Parabola Vertex" ], "new_concepts": [], "current_concepts": [ "Parabola Orientation", "Parabola Vertex", "Conic Sections" ] } ## Identify the parabola orientation and standard form $$ \begin{aligned} &\text{The parabola opens horizontally to the right.} \ &\text{Standard form for a horizontal parabola: } x = a(y - k)^2 + h \ &\text{where } (h, k) \text{ is the vertex.} \end{aligned} $$ ## Substitute the vertex coordinates $$ \begin{aligned} &\text{Given vertex: } (h, k) = (-2, 1) \ &x = a(y - 1)^2 - 2 \end{aligned} $$ ## Match with the given options $$ \begin{aligned} &\text{Comparing } x = a(y - 1)^2 - 2 \text{ with the options where } a = 4: \ &x = 4(y - 1)^2 - 2 \end{aligned} $$

A. $y = 4(x - 2)^2 - 1$

B. $x = 4(y - 1)^2 - 2$

C. $y = 4(x - 2)^2 + 1$

D. $x = 4(y + 1)^2 - 2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parabola Vertex" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the parabola orientation and standard form

Substitute the vertex coordinates

Match with the given options

Answer: