The function h = -6(t - 2.5)^2 + 38.5 gives the height, h metres, of a batted baseball as a function of the time, t seconds, since the ball was hit. What as the maximum height of the ball?

a) -6
b 2.5
c) 38.5
d) 0

38.5

h = -6(t - 2.5)^2 + 38.5

plug in a few values for t
when t = 1, h = 25
when t = 2, h = 37
when t = 2.5, h = 38
when t = 3, h = 37

you try, what do you think the answer is

38.5

To find the maximum height of the ball, we need to determine the vertex of the parabolic function. The vertex represents the highest or lowest point on the graph.

In this case, the given function is in the form h = a(t - b)^2 + c, where a, b, and c are constants.

Comparing this to the given function h = -6(t - 2.5)^2 + 38.5, we can see that:
- a = -6
- b = 2.5
- c = 38.5

The x-coordinate of the vertex is given by the formula x = -b / (2a). Plugging in the values we know, we get:
x = -2.5 / (2 * -6) = -2.5 / -12 = 5/24

We can substitute this value of x back into the original function to find the maximum height:
h = -6(5/24 - 2.5)^2 + 38.5
h = -6(5/24 - 60/24)^2 + 38.5
h = -6(-55/24)^2 + 38.5
h = -6(3025/576) + 38.5
h = -24.79 + 38.5
h ≈ 13.71

Therefore, the maximum height of the ball is approximately 13.71 meters.

The correct answer is not explicitly given among the options.