A water balloon is dropped from a height of 16 feet. The function h=-16x^2+16 gives the height h of the balloon after x seconds. When does it hit the ground?

The ballon will hit the ground after 1 s.

Step-by-step explanation:

In this case we want to solve for x, but were given a equation to the height of the ballon, we can organize it in a way that isolates x on the left side of the equation so it can be used to what we want. So we have:

h = - 16x^2 + 16

h + 16x^2 = 16

16x^2 = 16 - h

x^2 = (16 - h) / 16

x = sqrt (16 - h) / sqrt (16) = sqrt (16 - h) / 4

When the ballon hits the ground it's height is 0 feet, so we substitute that on our equation and we'll have the right answer.

x = sqrt (16 - 0) / 4 = sqrt (16) / 4 = 4/4 = 1 s