complete the square to find the vertex of this parabola.

\y^2 + 6y + 8x + 1 = 0\

(?, )

Question

complete the square to find the vertex of this parabola.

\y^2 + 6y + 8x + 1 = 0\

(?,  )

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Parabola Properties" ], "new_concepts": [ "Completing the Square for Parabolas" ], "current_concepts": [ "Parabola Properties", "Completing the Square for Parabolas" ] } ## Isolate the quadratic terms and complete the square $$ \begin{aligned} y^2 + 6y &= -8x - 1 \ y^2 + 6y + 9 &= -8x - 1 + 9 \ (y + 3)^2 &= -8x + 8 \end{aligned} $$ ## Write in standard vertex form $$ \begin{aligned} (y + 3)^2 &= -8(x - 1) \ x - 1 &= -\frac{1}{8}(y + 3)^2 \ x &= -\frac{1}{8}(y + 3)^2 + 1 \end{aligned} $$ ## Identify the vertex $(h, k)$ $$ \begin{aligned} h &= 1 \ k &= -3 \ \text{Vertex} &= (1, -3) \end{aligned} $$ Complete the square to find the vertex of this parabola. $$y^2+6y+8x+1=0$$ (1, -3) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Parabola Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the quadratic terms and complete the square

Write in standard vertex form

Identify the vertex \((h, k)\)

Answer: