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.

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.