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?
