determine the axis of symmetry and the vertex of the given function

(y = 2x^2 - 12x + 21)

axis of symmetry: (x = )

vertex: (( , ))

Question

determine the axis of symmetry and the vertex of the given function

(y = 2x^2 - 12x + 21)

axis of symmetry: (x = )

vertex: ((	, 	))

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Functions" ], "new_concepts": [ "Vertex of a Quadratic Function", "Axis of Symmetry" ], "current_concepts": [ "Quadratic Functions", "Vertex of a Quadratic Function", "Axis of Symmetry" ] } ## Find the axis of symmetry $$ \begin{aligned} &y = 2x^2 - 12x + 21 \quad (a = 2, \, b = -12, \, c = 21)\ &x = -\frac{b}{2a} = -\frac{-12}{2(2)} = 3 \end{aligned} $$ ## Calculate the vertex coordinates $$ \begin{aligned} &x = 3\ &y = 2(3)^2 - 12(3) + 21 = 18 - 36 + 21 = 3\ &\text{Vertex} = (3, 3) \end{aligned} $$ Determine the axis of symmetry and the vertex of the given function $y = 2x^2 - 12x + 21$ Axis of symmetry: $x =$ 3 Vertex: (3, 3) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Vertex of a Quadratic Function" ] }

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Question

Explanation:

Find the axis of symmetry

Calculate the vertex coordinates

Answer: