the vertex of the parabola below is at the point (2, -5). which of the equations below could be the one for this parabola?

a. (y = (x + 2)^2 - 5)
b. (y = (x + 5)^2 + 2)
c. (x = -4(y - 2)^2)
d. (y = (x - 2)^2 - 5)

Question

the vertex of the parabola below is at the point (2, -5). which of the equations below could be the one for this parabola?

a. (y = (x + 2)^2 - 5)
b. (y = (x + 5)^2 + 2)
c. (x = -4(y - 2)^2)
d. (y = (x - 2)^2 - 5)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Vertex Form of a Parabola" ], "new_concepts": [], "current_concepts": [ "Vertex Form of a Parabola", "Parabola Equation" ] } ## Identify the vertex form of a vertical parabola $$ y = a(x - h)^2 + k $$ ## Substitute the given vertex coordinates $$ \begin{aligned} (h, k) &= (2, -5) \ y &= a(x - 2)^2 - 5 \end{aligned} $$ ## Match with the given options $$ \begin{aligned} \text{For } a = 1: \quad y &= (x - 2)^2 - 5 \end{aligned} $$ This matches Option D.

A. $y = (x + 2)^2 - 5$

B. $y = (x + 5)^2 + 2$

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

D. $y = (x - 2)^2 - 5$

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

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QUESTION IMAGE

Question

Explanation:

Identify the vertex form of a vertical parabola

Substitute the given vertex coordinates

Match with the given options

Answer: