Answer:
The maximum height of the ball is 380.25 feet in the air.
Step-by-step explanation:
The quadratic function:
Models the ball's height <em>h(t)</em>, in feet, above the ground <em>t</em> 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, <em>a</em> = -16, <em>b</em> = 132, and <em>c</em> = 108. Find the <em>t-</em>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.
