What is the maximum height of the ball and when does it occur?
To find the maximum height of the ball, we need to find the vertex of the parabolic function h(t) = 3 + 34t - 16t^2, which represents the height of the ball as a function of time. The vertex has a t-coordinate of -b/2a, where a = -16 and b = 34.
t = -b/2a = -34/(2*(-16)) = 1.0625
To find the corresponding height, we substitute t = 1.0625 into the equation for h(t):
h(1.0625) = 3 + 34(1.0625) - 16(1.0625)^2 ≈ 43.015625
Therefore, the maximum height of the ball is approximately 43.015625 feet, and it occurs after 1.0625 seconds.