Question

A player hits a second baseball. The second baseballs path is modeled by the function g (t) = -16(t-4)^2 + 256. Which baseball has a greater maximum height? Which baseball is in the air for the longest?

Answer 1

1). Maximum height achieved by the baseball = 256 units

2). duration for which baseball is in the air = 8 seconds

Explanation:

A player hits a second baseball. Path of the baseball is defined by the function g(t) = -16(t - 4)² + 256

By comparing this equation with the quadratic function,

f(x) = a(x - h)² + k

Here, (h, k) is the vertex of the given equation.

Vertex of the given equation → (4, 256)

Therefore, maximum height the baseball can each = 256 units

And time taken to reach the maximum height = 4 seconds

So the duration of time in which baseball is in the air = Time taken to reach the maximum height + Time taken to come down from maximum height

= 4 + 4

= 8 seconds