Height in feet 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 we replace height f(x) by 0 and solve for x to find the time taken to reach the ground
[tex]f(x) = -16(x^2-5x-6)[/tex]
[tex]0= -16(x^2-5x-6)[/tex] ( divide by -16 on both sides)
[tex]0=(x^2-5x-6)[/tex]
Now factor it
(x-6)(x+1) =0
x-6 =0 and x+1=0
x=6 and x=-1
Time cannot be negative so we ignore -1
x = 6 seconds
It will take 6 seconds for the ball to reach the ground.
