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#### • equation to find axis of symmetry

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Question:The vertex and the axis of symmetry are related, but I am not sure how to explain it. Can someone help me. I know that you find them by using -b-4ac/2a, but that doesn't explain how they are related?

Answers:person above made mistake when calculating dy/dx axis of symmetry is the line x=-b/2a the vertex will ALWAYS lie on the axis of symmetry of a parabola and for his last point, axis of symmetry is x=a, NOT Y

Question:So I'm learning about quadratic equations and parabolas... and I'm just wondering, when I solve for my zeros, and I only get one zero (x-int.) the zero in this case (when there's only one of them) is the equation of the axis of symmetry, right? For example, I solve for my zeros and there is only one. It is 2. (x=2) The equation of the axis of symmetry is also x=2 and the vertex is also located at (2,0) right?

Answers:I suppose your right because for there to be one solution then the parabola would have to have its lowest point, or minimum, in direct contact to a point on the x axis. This point would be the vertex also the area of the line of symmetry

Question:Question 1. What is the domain and range of the quadratic equation y = x2 14x 52? a. Domain: All Real Numbers Range: y 7 b. Domain: All Real Numbers Range: y 7 c. Domain: All Real Numbers Range: y 3 d. Domain: All Real Numbers Range: y 3 Question 2. What are the x and y intercepts of the quadratic equation y = (x 3)2 25? Identify the x intercepts by graphing the quadratic equation. a. x intercepts: ( 2, 0) and (8, 0) y intercept: (0, 16) b. x intercepts: (2, 0) and ( 8, 0) y intercept: (0, 16) c. x intercepts: ( 2, 0) and (8, 0) y intercept: (0, 25) d. x intercepts: (2, 0) and ( 8, 0) y intercept: (0, 25) Question 3. Which of the following is the vertex of the quadratic equation y = 6x2 24x + 32? a. ( 2, 8) b. ( 2, 8) c. (2, 8) d. (2, 8) Question 4. What are the x and y intercepts of the quadratic equation y = 2x2 8x + 6? a. x intercepts: ( 3, 0) and ( 1, 0) y intercept: (0, 3) b. x intercepts: ( 3, 0) and ( 1, 0) y intercept: (0, 6) c. x intercepts: ( 3, 0) and ( 1, 0) y intercept: (0, 3) d. x intercepts: (3, 0) and (1, 0) y intercept: (0, 6) Question 5. Which of the following is the equation of the axis of symmetry of the quadratic equation y = 2x2 + 24x + 62? a. x = 6 b. x = 6 c. x = 10 d. x = 10 Question 6. What is the domain and range of the quadratic equation y = (x 5)2 + 10? a. Domain: All Real Numbers Range: y 5 b. Domain: All Real Numbers Range: y 5 c. Domain: All Real Numbers Range: y 10 d. Domain: All Real Numbers Range: y 10 Question 7. Which of the following is the equation of the axis of symmetry of the quadratic equation y = 2(x + 7)2 4? a. x = 7 b. x = 4 c. x = 4 d. x = 7 Question 8 Which of the following is the vertex of the quadratic equation y = 4(x + 6)2 + 2? a. (6, 2) b. ( 6, 2) c. (6, 2) d. ( 6, 2)

Answers:1) Domain is all real numbers y = x^2 14x 52 y = -(x^2 + 14x + 52) y = -(x^2 + 14x + 49) - 3 y = -(x + 7)^2 - 3 Range is all x <= -3. In set notation, the range is (-infinity, -3].

Question:Hey, If your axis of symmetry is 0, is your vertex automatically 0? thanks

Answers:The x value is automatically 0, but the y value needs to be solved for. In the equation ax^2+c, c will be your y value. Thus (0,c) is the vertex