what is the equation of the axis of symmetry of the graph of $y + 3x - 6 = -3(x - 2)^2 + 4$?

$x = \frac{3}{2}$

$x = -\frac{1}{6}$

$x = -2$

$x = 2$

Question

what is the equation of the axis of symmetry of the graph of $y + 3x - 6 = -3(x - 2)^2 + 4$?

$x = \frac{3}{2}$

$x = -\frac{1}{6}$

$x = -2$

$x = 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Axis of Symmetry", "Vertex of a Quadratic Function" ], "new_concepts": [], "current_concepts": [ "Axis of Symmetry", "Vertex of a Quadratic Function", "Quadratic Functions" ] } ## Rewrite the equation in standard form $$ \begin{aligned} y + 3x - 6 &= -3(x-2)^2 + 4 \ y + 3x - 6 &= -3(x^2 - 4x + 4) + 4 \ y + 3x - 6 &= -3x^2 + 12x - 12 + 4 \ y + 3x - 6 &= -3x^2 + 12x - 8 \ y &= -3x^2 + 9x - 2 \end{aligned} $$ ## Calculate the axis of symmetry $$ \begin{aligned} a &= -3, \quad b = 9 \ x &= -\frac{b}{2a} \ x &= -\frac{9}{2(-3)} \ x &= \frac{3}{2} \end{aligned} $$

(A) $x = \frac{3}{2}$

(B) $x = -\frac{1}{6}$

(C) $x = -2$

(D) $x = 2$

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

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Question

Explanation:

Rewrite the equation in standard form

Calculate the axis of symmetry

Answer: