27

select the correct answer.

what is the vertex of the quadratic function?

(f(x) = (x - 8)(x - 4))

(( -6, 4 ))

(( -4, 8 ))

(( 4, 8 ))

(( 6, -4 ))

Question

27

select the correct answer.

what is the vertex of the quadratic function?

(f(x) = (x - 8)(x - 4))

(( -6, 4 ))

(( -4, 8 ))

(( 4, 8 ))

(( 6, -4 ))

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", "Axis of Symmetry", "Parabola Key Features" ], "new_concepts": [], "current_concepts": [ "Quadratic Functions", "Axis of Symmetry", "Parabola Key Features" ] } ## Find the x-coordinate of the vertex using symmetry $$ \begin{aligned} x_1 &= 8, \quad x_2 = 4 \ x_v &= \frac{x_1 + x_2}{2} = \frac{8 + 4}{2} = 6 \end{aligned} $$ ## Calculate the y-coordinate of the vertex $$ \begin{aligned} y_v &= f(6) = (6 - 8)(6 - 4) \ y_v &= (-2)(2) = -4 \end{aligned} $$ ## State the vertex coordinates $$ (h, k) = (6, -4) $$

(A) (-6,4)

(B) (-4,8)

(C) (4,8)

(D) (6,-4)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Find the x-coordinate of the vertex using symmetry

Calculate the y-coordinate of the vertex

State the vertex coordinates

Answer: