Mathematics

Question


The function h(x) is quadratic and h(3) = h(–10) = 0. Which could represent h(x)?


h(x) = x2 – 13x – 30

h(x) = x2 – 7x – 30

h(x) = 2x2 + 26x – 60

h(x) = 2x2 + 14x – 60

2 Answer

  • It would be the last one, h(x) = 2x2 + 14x - 60. If you plug in either 3 or -10 for the x value, the answer comes out to 0. 
  • Answer:

    Option D.

    Step-by-step explanation:

    We can solve this question by finding the values of h(3) and h(-10) from each option given.

    Option A.

    h(x) = x² - 13x - 30

    h(3) = 3² - (13×3) - 30

          = 9 - 39 - 30

          = -60

    h(-10) = (-10)² - 13(-10) - 30

             = 100 + 130 - 30

             = 200

    Therefore, h(3) ≠ h(-10)

    Option B.

    h(x) = x² - 7x - 30

    h(3) = 3² - 7×3 - 30

          = 9 - 21 - 30

          = -42

    h(-10) = (-10)² - 7(-10) - 30

             = 100 + 70 - 30

             = 140

    h(3) ≠ h(-10)

    Option C.

    h(x) = 2x² + 26x - 60

    h(3) = 2(3)² + 26×3 - 60

          = 18 + 78 - 60

          = 36

    h(-10) = 2(-10)² + 26(-10) - 60

             = 200 - 260 - 60

             = -120

    h(3) ≠ h(-10)

    Option D.

    h(x) = 2x² + 14x - 60

    h(3) = 2(3)² + 14(3) - 60

          = 18 + 42 - 60

          = 0

    h(-10) = 2(-10)² + 14(-10) - 60

             = 200 - 140 - 60

             = 0

    h(3) = h(-10) = 0

    Therefore, option D is the answer.

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