Question

1. 4 points. A man throws a football upward into the air. The two equations belowmodel the height H(t) in feet of the ball after t seconds of being thrown.Form AH (t) = -8(t – 2)2 + 37Form BH(t)= -812 + 32t + 5Use the two forms to answer the questions below. Use your knowledge ofquadratic characteristics to support your answer.a. What is the football's maximum height? (2 pt)b. What was the initial height of the ball? (2 pts)

Answer 1

Form A

H(t) = -8(t – 2)² + 37

Form B

H(t)= -8t² + 32t + 5

a. From form A, the vertex of the parabola is at (2, 37). This means that the maximum height is 37 feet and it's reached after 2 seconds.

b. The initial height corresponds to t = 0 seconds. Replacing t = 0 into form B:

H(0)= -8(0)² + 32(0) + 5 = 5 ft

That is, the initial height was 5 ft