SOLUTION: Xavier shoots a basketball in which the height, in feet, is modeled by the following equation: h(t)= −4t2+10t+18 , where t is time, in seconds. What is the maximum height

If you have the formula for a height given to you as a function of time in the form


    h(t) = -at^2 + bt + c,    (1)


where "a", "b" and "c" are real numbers, a > 0, then in this formula



    (a)  the initial height is equal to the coefficient "c" value;


    (b)  the initial velocity is the coefficient  "b" in the formula;


    (c)  the coefficient "a" value is half of the gravity acceleration.

         For the Earth conditions, the gravity acceleration is g = 9.81 m/s^2, or 32 ft/s^2.


         THEREFORE, if you use meters for height, you should use the approximate value of g = 10 m/s^2.

         So, in this case  a =  = 5  (the numerical value).


         ALTERNATIVELY, if you use feet for height, you should use the approximate value of g = 32 ft/s^2.

         So, in this case  a =  = 16  (the numerical value).



    (d)  To find the height at the time moment "t", simply substitute the value of "t" into the formula (1) and calculate.


    (e)  To find the time "t" when the height has a given value h = , substitute  h =  into equation (1)

         and solve equation  


             h(t) = -at^2 + bt + c = .    (2)



    (f)  To find the time when the height is maximal, use the formula


              = .      (3)



    (g)  To find the maximal height, substitute the time value  t=   of the formula (3)  into the formula (1).