Answer:
The maximum height of the ball is 380.25 feet in the air.
Explanation:
The quadratic function:

Models the ball's height h(t), in feet, above the ground t seconds after it was thrown.
We want to determine the maximum height of the ball.
Note that this is a quadratic function. Therefore, the maximum or minimum value will always occur at its vertex point.
Since our leading coefficient is leading, we have a maximum point. So to find the maximum height, we will find the vertex. The vertex of a quadratic equation is given by:

In this case, a = -16, b = 132, and c = 108. Find the t-coordinate of the vertex:

So, the maximum height occurs after 4.125 seconds of the ball being thrown.
To find the maximum height, substitute this value back into the equation. Thus:

The maximum height of the ball is 380.25 feet in the air.