what is the axis of symmetry for the graph of $y - 4x = 7 - x^2$?

- $y = 2$
- $x = 2$
- $y = 11$
- $x = 11$

Question

what is the axis of symmetry for the graph of $y - 4x = 7 - x^2$?

- $y = 2$
- $x = 2$
- $y = 11$
- $x = 11$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Functions" ], "new_concepts": [ "Axis of Symmetry" ], "current_concepts": [ "Quadratic Functions", "Axis of Symmetry" ] } ## Rewrite the equation in standard form $$ \begin{aligned} y - 4x &= 7 - x^2 \ y &= -x^2 + 4x + 7 \end{aligned} $$ ## Identify coefficients $$ \begin{aligned} a &= -1 \ b &= 4 \ c &= 7 \end{aligned} $$ ## Calculate the axis of symmetry $$ \begin{aligned} x &= -\frac{b}{2a} \ x &= -\frac{4}{2(-1)} \ x &= 2 \end{aligned} $$

(A) $y = 2$

(B) $x = 2$

(C) $y = 11$

(D) $x = 11$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Axis of Symmetry" ] }

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QUESTION IMAGE

Question

Explanation:

Rewrite the equation in standard form

Identify coefficients

Calculate the axis of symmetry

Answer: