The height in feet of a projectile is given by the function h(t) = -16t^2+20t+9 where t represents the time in seconds after launch. What is the maximum height reached by the projectile?
-16t^2 + 20t + 9
Te time to reach the max height can be found as
-20 / [ 2 * -16] = -20/ -32 = 5/8 sec
Putting this back into the function we find the max height as
-16(5/8)^2 + 20(5/8) + 9 =
-16 ( 25/64) + 100/8 + 9 =
-400/64 + 100/8 + 9 =
-100/16 + 200/16 + 144/16 = 244/16 = 15.25 ft