Question

A ball is thrown into the air from a height of 9cm above the ground, and its height is given by S=128+32t-16t^2, where t is the time in seconds
1) find the values of t that makes S=0.
2) Do both of the values of t have meaning for this application? Explain why

Answer 1

-16t² + 32t + 128 = 0
-16t² + 64t - 32t + 128 = 0
-16t(t - 4) - 32(t - 4)
(-16t - 32)(t - 4) = 0
-16t -32 = 0      t - 4 = 0
-16t = 32          t = 4
t = -2

t = -2 and t = 4 are the values that makes S = 0.
Yes, because if you apply either of  these values alone, S will be 0.