A juggler tosses a ball into the air. The balls height, h and time t seconds can be represented by the equation h (t) = - 16t^2+40t+4. Suppose the juggler missed and ball hit the ground. Find the maximum height of the ball and time it took to reach the ground.

29 feet

2.6 seconds

Step-by-step explanation:

h (t) is a downwards parabola, so the maximum is at the vertex.

t = - b / (2a)

t = - 40 / (2*-16)

t = 1.25

h (1.25) = - 16 (1.25) ² + 40 (1.25) + 4

h (1.25) = 29

When the ball lands, h (t) = 0.

0 = - 16t² + 40t + 4

0 = 4t² - 10t - 1

t = [ - (-10) ± √ ((-10) ² - 4 (4) (-1)) ] / 2 (4)

t = (10 ± √116) / 8

t = (5 ± √29) / 4

t is positive, so:

t = (5 + √29) / 4

t ≈ 2.6