question 10 of 10

the vertex of this parabola is at (-3, -2). which of the following could be its equation?

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

Question

question 10 of 10

the vertex of this parabola is at (-3, -2). which of the following could be its equation?

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

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", "Horizontal Parabola Equation" ], "new_concepts": [], "current_concepts": [ "Parabola Vertex", "Horizontal Parabola Equation" ] } ## Identify the standard form of a horizontal parabola $$ x = a(y - k)^2 + h $$ ## Substitute the given vertex coordinates $$ \begin{aligned} &(h, k) = (-3, -2)\ &x = a(y - (-2))^2 + (-3)\ &x = a(y + 2)^2 - 3 \end{aligned} $$ ## Match with the given options $$ \begin{aligned} &\text{For } a = -2:\ &x = -2(y + 2)^2 - 3 \end{aligned} $$

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

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

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

(D) $x = -2(y - 2)^2 - 3$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the standard form of a horizontal parabola

Substitute the given vertex coordinates

Match with the given options

Answer: