Question

Its height in feet is represented by f(x)=-16(x^2-6x-16),where x is the number of seconds since the rock is thrown .the height of the rock is 0 feet when it hits water.how long doesit take the rock to hit the water

Answer 1

here we have
`f(x)` is the height represented in feet.

we need to at when height is zero what will be the time taken to hit the ground.

which means
`f(x)=0` we need to find x when f(x)=0.

`-16(x^2-6x-16)=0`

`(x^2-6x-16)=(0)/(-16) =0`

we need to use quadratic formula to find x. or factorisation.

if we factor out
`x^2-8x+2x-16=0`

`x(x-8)+2(x-8)=0`

where
`(x+2)(x-8)=0`

`x=-2,8`

where as time cannot be negative so x=8 is the time when height is zero.