SOLUTION: If a football is kicked straight up with an initial velocity of 96ft/sec from a height of 5ft, then its height above the earth is a function of a time given by h(t)=-16t^2+96t+5.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: If a football is kicked straight up with an initial velocity of 96ft/sec from a height of 5ft, then its height above the earth is a function of a time given by h(t)=-16t^2+96t+5.      Log On


   

Question 54311: If a football is kicked straight up with an initial velocity of 96ft/sec from a height of 5ft, then its height above the earth is a function of a time given by
h(t)=-16t^2+96t+5. What the is the maximum height reached by the ball?
do I use the quad. formula or complete the square and please help me solve this. I'm utterly lost and needs the homeword turned in an hour. Thank you so much in advance!!
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
You can do either. The quadratic formula was derived by completing the square, I could bore you by proving that, but you only have an hour, besides that only helps you to find the time it takes for it to hit the ground! What you need is the vertex of this parabola (that's the maximum height). You can find this two ways:
h(t)=-16t^2+96t+5 is in ax^2+bx+c form.
The value for t in the vertex is found by the formula highlight%28t=-b%2F%282a%29%29.
Take that value and plug it back in for t in your t function. This will be the max height of the ball.
:
The second way is to put this in vertex form, you do this by completing the square.
highlight%28h%28t%29=a%28t-h%29%5E2%2Bk%29%29 (h,k) is the vertex and k is the Maximium height.
Good Luck!
Happy Calculating!!!