Question

A baseballs height in feet t seconds after it is hit is given by f(t) = -16t^2 + 132t + 4

Find f(3) and explain its meaning in the context of this problem.
When did the ball reach its maximum height?
What is the maximum height of the ball?

Answer 1

f(3) = -16(3)^2 + 132(3) + 4 = 376
The height of the baseball 3 seconds after it was hit is 376 feet.

The ball reaches its maximum height at the vertex of the parabola. The x-coordinate of the vertex is given by -b/2a, where a = -16 and b = 132. Therefore, the x-coordinate of the vertex is x = -b/2a = -132/(2(-16)) = 4.125 seconds.

To find the maximum height, we can substitute this value of x into the equation for f(t):

f(4.125) = -16(4.125)^2 + 132(4.125) + 4 = 275.5

Therefore, the ball reaches its maximum height after 4.125 seconds, and the maximum height of the ball is 275.5 feet.