Question

I need someone to explain to me the difference in the answer I got and the options that were given to me!

h = -16t2 + 36t + 4.

Answer 1

So the question was this: If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = -16t2 + 36t + 4.

I got this answer...\[9+-\frac{ \sqrt{97}}{ 8 }\]

Answer 2

the other option that made me second guess was this....\[\frac{ 9+-\sqrt{97} }{ 8 }\]
Now I don't know which one to choose

Answer 3

The Quadratic formula\[ax^2+bx+c=0\]\[x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

\[-16x^2+36x+4=0\]\[x_{1,2}=\frac{-36\pm\sqrt{36^2-4(-16)(4)}}{2(-16)}\\\qquad=\frac{-36\pm\sqrt{1296+256}}{-32}\\\qquad=\frac{-36\pm\sqrt{1552}}{-32}\\\qquad=\frac98\pm\frac{\sqrt{1552}}{-32}\\\qquad=\frac98\pm\frac{\sqrt{1552/4^2}}{-8}\\\qquad=\frac98\pm-\frac{\sqrt{97}}8\\\qquad=\frac18(9\mp\sqrt{97})\]

Answer 4

So its the second option!?

Answer 5

the square root of 97 is a bit larger than 9, so one solution to that equation will be negative, the other will be positive,

the negative solution will not fit the original question, because the football is moving forward with time

Answer 6

yeah\[x=\frac{ 9+\sqrt{97} }8\]
is the solution you are looking for

Answer 7

Thanks for breaking it down so well! I get it now!!

Answer 8

If you plot the equation

you'll see that the negative solution is what you get if the football was traveling along the same parabola before it got the the footballer