The height h (in feet) of an object thrown vertically upward from a tower 144 feet tall is given by h=144+128t-16t², where t measures the time in seconds from the time when the object is released. how long does it take for the object to reach the ground?

It takes 9 seconds to hit the ground.

Setting the equation equal to 0, we have:

0 = 144 + 128t - 16t²

Factoring out the GCF, we have

0 = 16 (9 + 8t - t²)

Factoring out - 1, we have:

0 = - 16 (-9 - 8t + t²)

In standard form, this is

-16 (t² - 8t - 9) = 0

This is easily factorable; - 9 (1) = - 9 and - 9+1 = - 8:

-16 (t-9) (t+1) = 0

Using the zero product property, we know either t-9=0 or t+1=0; therefore t=9 or t=-1. Since negative time makes no sense, t=9.