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A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t2 + 576t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit. i don't even understand what she is wanting me to do??????????

Mathematics
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How ois the Physics question posted here @.Sam.
math books have these types of questions as well
its asking you for the vertex of the parabola

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Other answers:

if you can find the roots, you can determine the t value as the middle of the roots
i Don't understand how to get to the vertex
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can you find where the zeros for it are?
No
then you are clearly not prepared to tackle this problem.
can you factor the given equation?
yes i got to 16(t^2 + 36t)
pull out a t as well
16t(t+36) = 16t (t+6) (t-6)
16t (t+36) is as far as you can go now the key here is to remember your zero times tables ....
okay
16t (-t+36) = 0 when 16t=0, or when -t+36 = 0 what values do we get for "t"?
if 16t=0 then t is 0 and if -t+36=0 then -t=-36
good, so lets say it takes from t= 0 to 36 seconds to go up and come back down to the ground. (h=0) the great thing about a parabola is that it takes the same amount of time to go up as it does to go down. the highest point is therefore, half of the time interval. what is half way between 0 and 36 ?
18
good, then it takes 18 seconds for it to reach its maximum position, and another 18 seconds to fall back down to the ground
thank you :)
good luck :)
h(t)=-16t^2+576t \[\frac{ dh }{ dt }=-32t+576\] when it is at maximum height dh/dt =0 -32t+576=0,t=576/32=18 sec. when t=18 sec., h=-16*18*18+576=18(-16*18+32)=18*32(-9+1)=576*-8=-4608 maximum height reached=4608 units.

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