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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?

Respuesta :

The ball takes 6 seconds to reach the ground.

Explanation

Height of the ball after [tex]x[/tex] seconds is represented by....

[tex]f(x)= -16(x^2 -5x-6)[/tex]

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 [tex]f(x)=0[/tex] into the above equation and then solve for [tex]x[/tex].

Thus...

[tex]0=-16(x^2-5x-6)\\ \\ x^2-5x-6=0\\ \\ (x-6)(x+1)=0[/tex]

Using zero-product property....

[tex]x-6=0\\ x=6[/tex]

and

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

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

six seconds (apex) :)

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