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

Answer 1

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 2

Option D.

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.