Question

The motion of the ball from the time it was thrown upwards was modeled closely by the function,h(t)=-16t2+128t+144, where h(t) represents the height of the ball in feet after t seconds. After how many seconds did the ball reach the ground?

please I need help

Answer 1

9 seconds

Explanation:

When the ball reaches the ground, the height, h(t), is 0. Might as well make the numbers easier to work with - since for the x-intercepts (t-intercepts), h(t) = 0, you can divide the entire equation by the greatest common factor, in this case -16, to make things better:

`0=-16t^2+128t+144\\0=t^2-8t-9`

Now you can solve this any way you like, such as by using:

`(-b \± √(b^2-4ac))/(2a)\\`

This is an easy polynomial though, and you may be able to factor it just by eyeballing it:

`0=t^2-8t-9\\0=(t-9)(t+1)\\t=9,-1`

You can't have negative time, so we reject -1, leaving only 9 as the answer.