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# help

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A ball travels on a parabolic path in which the height (in feet) is given by the expression \(-16t^2+64t+31\), where \(t\) is the time after launch. What is the maximum height of the ball, in feet?

Jul 30, 2019

#1
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h  =  -16t2 + 64t + 31

maximum value of  h  will occur when    t  =  -b / [2a]

that is, when   t  =  -64 / [ 2(-16) ]

Once you know the value of  t  that produces the maximum value of  h ,

plug that value in for  t  to find the height at that time.

Can you finish it? If you get stuck let us know.

Jul 30, 2019
#2
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I'm stuck i got t = 2 but what do I do from now.

Jul 31, 2019
#3
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Since the max height occurs at t = 2

Just stick 2 into the function for t   and evaluate

So....you are evaluating

-16(2)^2  + 64(2)  + 31      =   max height

Can you take it from here, Logic ????   CPhill  Jul 31, 2019
#4
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Thanks hectictar and CPhill I got 95 is that correct?!?

Jul 31, 2019
#5
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Yes, that is correct! Here's a graph of the equation   h  =  -16t2 + 64t + 31

where you can see that the maximum value of  h  is  95  and it occurs when  t = 2

https://www.desmos.com/calculator/wtrtbakdpy

hectictar  Jul 31, 2019