Multiple choice

y = d(x - 3)(x + 5) In the quadratic equation above, d is a non-zero constant. The graph of the equation in the xy-plane is a parabola with vertex (e, f). Which of the following is equal to f?

  1. 9d

  2. 25d

  3. -16d

  4. -4d
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C Correct answer
Explanation

The roots are 3 and -5. The x-coordinate of the vertex is the midpoint of the roots: (3 + -5) / 2 = -1. The y-coordinate f is d(-1 - 3)(-1 + 5) = d(-4)(4) = -16d.

AI explanation

Using the formula for the vertex x-coordinate, e = -b / (2a) = -2d / (2d) = -4. Substituting this back into the equation to find f gives f = d((-4) - 3)((-4) + 5) = d(-7)(1). This calculates to -16d.

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