question 2 of 10

the vertex of this parabola is at (-2, 5). which of the following could be its equation?

a. (y = 3(x - 2)^2 + 5)
b. (y = 3(x - 2)^2 - 5)
c. (y = 3(x + 2)^2 - 5)
d. (y = 3(x + 2)^2 + 5)

Question

question 2 of 10

the vertex of this parabola is at (-2, 5). which of the following could be its equation?

a. (y = 3(x - 2)^2 + 5)
b. (y = 3(x - 2)^2 - 5)
c. (y = 3(x + 2)^2 - 5)
d. (y = 3(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": [ "Parabola Vertex" ], "new_concepts": [], "current_concepts": [ "Parabola Vertex", "Parabola Orientation" ] } ## Identify vertex form of a parabola $$ y = a(x - h)^2 + k $$ ## Substitute the given vertex coordinates $$ \begin{aligned} &(h, k) = (-2, 5)\ &y = a(x - (-2))^2 + 5\ &y = a(x + 2)^2 + 5 \end{aligned} $$ ## Match with the given options $$ \begin{aligned} &a = 3 > 0 \quad \text{(opens upward)}\ &y = 3(x + 2)^2 + 5 \end{aligned} $$

A. $y = 3(x - 2)^2 + 5$

B. $y = 3(x - 2)^2 - 5$

C. $y = 3(x + 2)^2 - 5$

D. $y = 3(x + 2)^2 + 5$

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

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QUESTION IMAGE

Question

Explanation:

Identify vertex form of a parabola

Substitute the given vertex coordinates

Match with the given options

Answer: