SOLUTION: A player throws a ball straight up toward the roof of a gym. The height hin feet of the ball after tseconds can be modeled by the function h(t)=-16t^2+55t+4 a. The height of the

f.  How long will it take to reach the maximum height?


    It is about finding the maximum of the quadratic function  

        h(t) = -16t^2 + 55t + 4.     (1)

    Use the formula   = ,  where  "a"  is the coefficient at the quadratic term 
    and  "b"  is the coefficient at the linear term.




e.  What is the maximum height the ball will reach?


    Substitute the value of  ,  found in part f), into the formula (1).

    In this way, you will find the value of  .




a.  The height of the gym roof is 53 feet. Will the ball hit the ceiling?


    Compare the value of  , found in part e) above with the height of the celling of 53 ft.




b.  How long will it take for the ball to reach a height of 29 feet?


    To answer this question, solve the equation  -16t^2 + 55t + 4 = 29.




c.  How high will the ball be 3 seconds after it’s thrown?


    To answer this question, substitute the value of  t= 3 seconds into the formula (1).




d.  How high will be ball be 6.5 seconds after it’s thrown?


    To answer this question, substitute the value of  t= 6.5 seconds into the formula (1)

    If the result is greater than zero, then it is real height.

    If the result is negative, then the answer is h(t) = 0, which means "the ball just reached the floor".