Question

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?

Answer 1

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.