what are the coordinates of the vertex of the graph of $y = x^2 - 2x - 8$?

a. $(1, -8)$
b. $(1, -9)$
c. $(2, -8)$
d. $(1, -7)$

Question

what are the coordinates of the vertex of the graph of $y = x^2 - 2x - 8$?

a. $(1, -8)$
b. $(1, -9)$
c. $(2, -8)$
d. $(1, -7)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Finding Vertex of Quadratic" ], "new_concepts": [], "current_concepts": [ "Finding Vertex of Quadratic", "Graphing Quadratic Functions" ] } ## Identify coefficients of the quadratic equation $$ \begin{aligned} &y = x^2 - 2x - 8\ &a = 1,\quad b = -2,\quad c = -8 \end{aligned} $$ ## Calculate the x-coordinate of the vertex $$ x = -\frac{b}{2a} = -\frac{-2}{2(1)} = 1 $$ ## Calculate the y-coordinate of the vertex $$ y = (1)^2 - 2(1) - 8 = 1 - 2 - 8 = -9 $$

A. (1, -8)

B. (1, -9)

C. (2, -8)

D. (1, -7)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Finding Vertex of Quadratic" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients of the quadratic equation

Calculate the x-coordinate of the vertex

Calculate the y-coordinate of the vertex

Answer: