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y = a(x + 3)(x - 1)
In the quadratic function above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (m, n). Which of the following is equal to n?
In the quadratic function above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (m, n). Which of the following is equal to n?
- a)0
- b)2a
- c)-2a
- d)-4a
Correct answer is option 'D'. Can you explain this answer?
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y = a(x + 3)(x - 1)In the quadratic function above, a is a nonzero con...
Original equation: y = a(x + 3)(x - 1)
This equation represents a quadratic in x. Since it is in factored form, it shows us that the function has x-intercepts (also known as zeroes or roots) when x 1 3 = 0 or x - 1 = 0, so its x-intercepts are at x = -3 and x = 1. Recall (from Chapter 9, Lesson 6) that a parabola representing a quadratic function has an axis of symmetry at x = k, where k is midway between the x-intercepts. Therefore, k = (-3 + 1)/2 = -1. This axis of symmetry, x = -1, must pass through the vertex. We can get the y-coordinate of this vertex by just plugging x = -1 back into the function: y = a(- 1 + 3)(-1 - 1)
Simplify: y = a(2)(-2) = -4a
This equation represents a quadratic in x. Since it is in factored form, it shows us that the function has x-intercepts (also known as zeroes or roots) when x 1 3 = 0 or x - 1 = 0, so its x-intercepts are at x = -3 and x = 1. Recall (from Chapter 9, Lesson 6) that a parabola representing a quadratic function has an axis of symmetry at x = k, where k is midway between the x-intercepts. Therefore, k = (-3 + 1)/2 = -1. This axis of symmetry, x = -1, must pass through the vertex. We can get the y-coordinate of this vertex by just plugging x = -1 back into the function: y = a(- 1 + 3)(-1 - 1)
Simplify: y = a(2)(-2) = -4a
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y = a(x + 3)(x - 1)In the quadratic function above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (m, n). Which of the following is equal to n?a)0b)2ac)-2ad)-4aCorrect answer is option 'D'. Can you explain this answer?
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