suppose h(t)= -0.2t^2 + 2t models the height, in feet, of the ball that is kicked in the air where t is given as time, in seconds

Question

After how many seconds does the ball reach its maximum height?

What is the maximum height of the ball?

After how many seconds does the ball reach the ground?

Answer 1

You can easily solve this by graphing the function. Remember that height is how high (up) something is, so you would calculate the maximum point and identify the y value. Keep in mind that the y-axis goes up and down. Then, time is independent, which is the x-values, so the x-value in each point represents the time in seconds at that particular point/height. Last, think of image when something is on the ball, in a graph that ground is represented by the x-axis. The reason is any point below the x-axis represent a negative height, but there's no such thing in the real world.

When graphing you, you find the following:

The maximum point is (5,5)

Seconds to reach maximum height: 5 seconds

Maximum height: 5 feet

The x-intercept/root/zero is (10, 0)

Second to reach the ground: 10 seconds