How Do You Interpret Inputs and Outputs for a Model?

In the example below, we want to look at the inputs and outputs for a function and interpret what they tells us. In both examples, the function is a quadratic function that models the rise and fall of an object thrown in the air.

Example 1 Suppose a ball is thrown into the air has its height (in feet) given by the function

$latex \displaystyle h(t)=6+128t-16{{t}^{2}}$

a. Find h(1) and explain what it means.

b. Find the height of the ball 4 seconds after it is thrown.

c. Test other values of  to decide if the ball eventually falls. When does the ball stop climbing?