# Solving the polynominal: $s(t) = -16t^2 + 48t + 160$

The height of a ball is thrown directly upward from an initial height of $160$ ft with an initial velocity of $48$ ft per second is given by the function:

$s(t) = -16t^2 + 48t + 160$, where $s(t)$ gives the ball's height above ground in feet, $t$ seconds after it is thrown. How long will it take for the ball to hit the ground?

• What are your thoughts on the problem? – Peter Woolfitt Jul 8 '14 at 5:28
• I need help in trying to solve it. I do not know where to start. Do I start by factoring it out? – thes4s Jul 8 '14 at 5:30
• Divide it all by 16, and try to factorise it then. It comes out nicely. – user105475 Jul 8 '14 at 5:30
• When the ball hits the ground $s(t)=0$. How do you solve such kind of equations? – Hassan Muhammad Jul 8 '14 at 5:32
• So it becomes s(t) = -t^2 + 3t + 10 – thes4s Jul 8 '14 at 5:32

HINT

You have a quadratic so, if you factor it and you will find the roots or in other words, when the balls hits the ground.

HINT $2$

You can factorize your polynomial by dividing by $-16$ and finding two numbers which add to $-3$ and multiply to $-10$

HINT $3$

Your answer should be in the form $-16(x-a)(x+b)$ where $a$ and $b$ are the numbers which make your equation zero or in other words, the roots.

• I divided it by 16. and got s(t)= -t^2+3t+10. Then I factored it and got (-t-2)(t-5) so the answer is 5 correct? – thes4s Jul 8 '14 at 5:37
• You should also take out the negative sign from $s(t)$ and you will get a similar answer: $-16(t+5)(t-2)$ – Jeel Shah Jul 8 '14 at 5:42
• I understand it now. thank you! – thes4s Jul 8 '14 at 5:45
• @gekkostate It should be $-16(t-5)(t+2)$. – Peter Woolfitt Jul 8 '14 at 5:47
• Anytime! I'm not sure if you have visited the help center or seen the FAQ but if you notice, there is a small check mark beside this answer and any other answer you will see on this website. There is also an upvote button and a downvote button. When you have 15 rep, you can upvote and downvote an answer. Also, if you hit the checkmark then the answer will be accepted and will close a "loop" so to speak. – Jeel Shah Jul 8 '14 at 5:48