Question

Rachel is about to serve and tosses a tennis ball straight up into the air. The height, h, of the ball, in meters at a time t, is given by h(t) = -5t² + 5t + 2. Will the ball reach a height of 4 meters? Will it reach a height of 3 meters? Why or why not?

1) Yes, the ball will reach a height of 4 meters.
2) No, the ball will not reach a height of 4 meters.
3) Yes, the ball will reach a height of 3 meters.
4) No, the ball will not reach a height of 3 meters.

Answer 1

To determine if the ball will reach a height of 4 meters or 3 meters, we can solve the given quadratic equation for t and check for real solutions. If there are real solutions, then the ball will reach that height.

Step-by-step explanation:

The given quadratic function for the height of the ball, h(t) = -5t² + 5t + 2, can be used to determine if the ball will reach a height of 4 meters or 3 meters.

To find out if the ball will reach a height of 4 meters, we need to solve the equation h(t) = 4 for t. Substitute 4 for h(t) in the equation and solve for t. If there are any real solutions, then the ball will reach a height of 4 meters. Repeat the same process for the height of 3 meters.

If we find any real solutions for t in both cases, then the respective height will be reached by the ball. Otherwise, if there are no real solutions for t, then the ball will not reach that height.