Question

Scott kicks a soccer ball during a game. The height of the ball, in feet, can be modeled by the function f(x) = -16x^2 + 48x, where x is the time in seconds after he kicks the ball.

When does this occur?

A) After 1.5 seconds
B) After 2 seconds
C) After 3 seconds
D) After 4 seconds

Answer 1

To determine when the ball reaches a certain height, we need to find the time at which the height function is equal to that height. In this case, the height we are interested in is 0, since the ball is on the ground. So we need to solve the equation f(x) = -16x^2 + 48x = 0. The ball hits the ground after 3 seconds.

Step-by-step explanation:

To determine when the ball reaches a certain height, we need to find the time at which the height function is equal to that height. In this case, the height we are interested in is 0, since the ball is on the ground. So we need to solve the equation f(x) = -16x^2 + 48x = 0. We can factor out -16x and solve for x, giving us x = 0 and x = 3. Since the height of the ball is 0 when x = 0 and x = 3, the ball hits the ground after 3 seconds.