what is the vertex of the graph of (y + 2x + 3 = -(x + 2)^2 + 1)?

* ((-3, -33))
* ((-3, 3))
* ((3, -24))
* ((3, 21))

Question

what is the vertex of the graph of (y + 2x + 3 = -(x + 2)^2 + 1)?

* ((-3, -33))
* ((-3, 3))
* ((3, -24))
* ((3, 21))

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Vertex of a Quadratic Function" ], "new_concepts": [], "current_concepts": [ "Vertex of a Quadratic Function", "Quadratic Functions" ] } ## Isolate y in the given equation $$ \begin{aligned} y + 2x + 3 &= -(x + 2)^2 + 1 \ y &= -(x + 2)^2 + 1 - 2x - 3 \ y &= -(x^2 + 4x + 4) - 2x - 2 \ y &= -x^2 - 6x - 6 \end{aligned} $$ ## Find the x-coordinate of the vertex $$ \begin{aligned} x_v &= -\frac{b}{2a} \ x_v &= -\frac{-6}{2(-1)} = -3 \end{aligned} $$ ## Find the y-coordinate of the vertex $$ \begin{aligned} y_v &= -(-3)^2 - 6(-3) - 6 \ y_v &= -9 + 18 - 6 = 3 \end{aligned} $$

(-3, -33)

(-3, 3)

(3, -24)

(3, 21)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Vertex of a Quadratic Function" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate y in the given equation

Find the x-coordinate of the vertex

Find the y-coordinate of the vertex

Answer: