Question

The function y= -16t^2 +24t represents the height y (in feet) of a tennis ball bouncing straight up from the ground t seconds after it bounces. After how many seconds does the tens ball return to the ground?

Answer 1

We want to know the time, t, it takes the ball to reach a height (y) of 0.
$0=-16t^2+24t$
We can factor out the GCF first.  The largest number that will divide evenly into 16 and 24 is 8.  Also, both terms have a t, so we can factor that out as well:
$0=8t(-2t+3)$ (-16/8 = -2 and 24/8 = 3)
Using the zero product property, we know that either 8t=0 or -2t+3=0.  Solving the first equation, we would divide both sides by 8:
8t/8=0/8
t=0
This is at 0 seconds, before the ball is in the air at all.
Solving the second equation, we start by subtracting 3 from both sides:
-2t+3-3=0-3
-2t=-3
Now we divide both sides by -2
-2t/-2=-3/-2
t=1.5
After 1.5 seconds, the ball will hit the ground again.