Question

The height of a ball thrown upward from the ground is given by the quadratic function

h = 120t - 16t2, where h is in feet and t is in seconds.

What is the reasonable range for this function?

Answer 1

h = 120t - 16t² <===> h=-16t²+120t (ax²+bx+c)
Since a<0 it has a maximum
1st calculate its axis of symmetry: = -b/2a = -120/(-)32 = 120/32=15/4 =3.75
So the axis of symmetry is x=3.75
The maximum range is on this axis. Plug its value (3.75) into the equation & you will find h = 120(3.75) -120(3.75)² = 225

H has a maximum range (height) equal to 225