Question

A ball is thrown in the air from a ledge. Its height in feet is represented by f(x) = –16(x2 – 5x – 6), where x is the number of seconds since the ball has been thrown. The height of the ball is 0 feet when it hits the ground. How many seconds does it take the ball to reach the ground?

Answer 1

six seconds (apex) :)

Answer 2

The ball takes 6 seconds to reach the ground.

Step-by-step explanation

Height of the ball after
`x` seconds is represented by....

`f(x)= -16(x^2 -5x-6)`

The height of the ball is 0 feet when it hits the ground. So, for finding the number of second the ball takes to reach the ground, we will just plug
`f(x)=0` into the above equation and then solve for
`x`.

Thus...

`0=-16(x^2-5x-6)\\ \\ x^2-5x-6=0\\ \\ (x-6)(x+1)=0`

Using zero-product property....

`x-6=0\\ x=6`

and

`x+1=0\\ x=-1` (Negative value is ignored as time can't be negative)

So, the ball takes 6 seconds to reach the ground.