8
advanced-math

The path of a basketball is y=−0.1x2+x+6y = -0.1x^2 + x + 6, where x is horizontal distance. How far does it travel horizontally before hitting the ground?

A

14.4 ft

B

10 ft

C

5 ft

D

20 ft

Correct Answer: A

Choice A is the correct answer. Solve −0.1x2+x+6=0-0.1x^2 + x + 6 = 0.

  1. Multiply by -10: x2−10x−60=0x^2 - 10x - 60 = 0.
  2. Quadratic formula: x=10±100−4(1)(−60)2x = \frac{10 \pm \sqrt{100 - 4(1)(-60)}}{2}.
  3. x=10±3402≈10±18.442x = \frac{10 \pm \sqrt{340}}{2} \approx \frac{10 \pm 18.44}{2}.
  4. Positive root: x≈28.44/2=14.22x \approx 28.44 / 2 = 14.22. Closest option is 14.4.

Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Next
Question 9 →
Back to Set
Set 17: Quadratic Equations and Functions 17