The Hornets' all-state quarterback threw a pass on the run, straight toward the goal line 40 yards away. Unfor

Question

The Hornets' all-state quarterback threw a pass on the run, straight toward the goal line 40 yards away. Unfortunately, no players were near the goal line. The ball was 2 yards above the ground when he released it, and it followed the parabolic path f(x)= -0.03x^2 + 1.2x + 2, with f(x) representing the height of the ball in yards and x representing the number of yards traveled toward the goal line.

a. What was the maximum height the ball reached? Where did this happen?

b. What was the height of the ball when (and if) it reached the goal line?

c. Where did it hit the ground?

Answer 1

f(x)= -0.03x^2 + 1.2x + 2

f(x)= -0.03(x^2 - 40x) + 2

f(x)= -0.03(x^2 - 40x + 20^2 - 400) + 2

f(x)= -0.03(x - 20)^2 + 12 + 2

f(x)= -0.03(x - 20)^2 + 14

a. max height was 14 yards at 20 yards away.

b. height at goal line was 2 yards

c. - 0.03(x - 20)^2 + 14 = 0

0.03(x - 20)^2 = 14

(x - 20)^2 = 466.666667

x - 20 ≈ 21.6

x ≈ 41.6, or 1.6 yards past the goal line