Multiple choice

Y = a(x + 3)(x – 5) In the quadratic equation above, a is a nonzero constant. The graph of the equation in the xy- plane has the vertex (h, k). If the value of k is -8, what is the value of a?

  1. ¾

  2. ½

  3. 5/8

  4. 4/6
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B Correct answer
Explanation

The vertex x-coordinate h is the midpoint of the roots -3 and 5, so h = (-3+5)/2 = 1. The vertex is (1, k). Given k = -8, substitute into the equation: -8 = a(1+3)(1-5) = a(4)(-4) = -16a. So a = -8 / -16 = 1/2.

AI explanation

The axis of symmetry for the parabola is the midpoint of the x-intercepts, so h = (-3 + 5)/2 = 1. We substitute x = 1 into the equation to find the y-coordinate of the vertex, giving k = a(1 + 3)(1 - 5) = -16a. We are given that k = -8, so we set -16a = -8. Solving for a gives a = 1/2.

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