Question

The height of a kicked soccer ball can be modeled by the following quadratic function: (h = -2(t - 5)^2 + 24), where h is the height in meters and t is the time in seconds. What is the maximum height that the ball was kicked?

a) 24 meters
b) 16 meters
c) 10 meters
d) 8 meters

Answer 1

To find the maximum height of the kicked soccer ball, we look at the vertex of the quadratic function. The vertex form of the function immediately indicates that the maximum height is 24 meters.

Step-by-step explanation:

The maximum height that a soccer ball reaches in its flight can be determined by examining the quadratic function modeling its trajectory. For the given function h = -2(t - 5)² + 24, the maximum height is the vertex of the parabola, which represents the peak of the ball's path. Since the function is already in vertex form, where the vertex (h, t) is (24, 5), we can see that the maximum height, which is the value of h at the vertex, is 24 meters.

Therefore, the correct answer to the question, 'What is the maximum height that the ball was kicked?' is a) 24 meters. This is when the time, t, is at 5 seconds, just before the ball starts descending due to gravity.