what is the vertex and the equation of the axis of symmetry of the graph of (y = x^2 - 6x - 7)?

- vertex: ((3, -16)), a.o.s: (x = 3)
- vertex: ((20, -3)), a.o.s: (x = 20)
- vertex: ((-3, 20)), a.o.s: (x = -3)
- vertex: ((-16, 3)), a.o.s: (x = -16)

Question

what is the vertex and the equation of the axis of symmetry of the graph of (y = x^2 - 6x - 7)?

- vertex: ((3, -16)), a.o.s: (x = 3)
- vertex: ((20, -3)), a.o.s: (x = 20)
- vertex: ((-3, 20)), a.o.s: (x = -3)
- vertex: ((-16, 3)), a.o.s: (x = -16)

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": [], "current_concepts": [ "Quadratic Functions", "Vertex of a Parabola", "Axis of Symmetry" ] } ## Find the x-coordinate of the vertex and axis of symmetry $$ \begin{aligned} &y = x^2 - 6x - 7 \ &a = 1, \quad b = -6, \quad c = -7 \ &x = -\frac{b}{2a} = -\frac{-6}{2(1)} = 3 \ &\text{a.o.s.: } x = 3 \end{aligned} $$ ## Find the y-coordinate of the vertex $$ \begin{aligned} &y = (3)^2 - 6(3) - 7 \ &y = 9 - 18 - 7 \ &y = -16 \ &\text{vertex: } (3, -16) \end{aligned} $$

vertex: $(3, -16)$ a.o.s.: $x = 3$

vertex: $(20, -3)$ a.o.s.: $x = 20$

vertex: $(-3, 20)$ a.o.s.: $x = -3$

vertex: $(-16, 3)$ a.o.s.: $x = -16$

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

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Question

Explanation:

Find the x-coordinate of the vertex and axis of symmetry

Find the y-coordinate of the vertex

Answer: