The function given by represents the height of a ball, in feet, seconds after it is thrown. To the nearest foot, what is the maximum height the ball reaches?
Select an Answer
The correct answer is D.
One way to determine the maximum height the ball reaches is to rewrite the quadratic expression that defines the function by completing the square:
It is not necessary to simplify any further, as the maximum height must correspond to , which is the only value of that makes the term nonnegative. By substitution, . Therefore, to the nearest foot, the maximum height the ball reaches is feet.
Alternatively, one can use a graphing calculator to determine the maximum value of the function . Since , and , the maximum value of must occur for some between and . Set the window so that the independent variable goes from to and the dependent variable goes from to to view the vertex of the parabola. Upon tracing the graph, the maximum value of is slightly greater than . Therefore, to the nearest foot, the maximum height the ball reaches is feet.