Example:

A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function . How long does it take the baseball to reach its maximum height? What is the maximum height obtained by the baseball?

Solution:

is defined to be a quadratic function. The graph of a quadratic function is a parabola. This quadratic function has a leading coefficient of -4.9 which means that the parabola is opening down.

Find the vertex to find the maximum value.

The ball reaches the maximum height 1.5 seconds after the ball was hit.

The maximum height can be found by substituting 1.5 seconds for time in the height function.

The maximum height of the ball is 12.025 meters.