SOLUTION: you throw a basketball up in the air. the basketball's height in feet, is given by the function h=-16t^2+30t+4, where t is the time in seconds after the ball leaves your hand.find

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Question 252853: you throw a basketball up in the air. the basketball's height in feet, is given by the function h=-16t^2+30t+4, where t is the time in seconds after the ball leaves your hand.find the greatest height the ball reaches.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The max height is at the vertex.




In order to find the vertex, we first need to find the t-coordinate of the vertex.


To find the t-coordinate of the vertex, use this formula: t=%28-b%29%2F%282a%29.


t=%28-b%29%2F%282a%29 Start with the given formula.


From h=-16t%5E2%2B30t%2B4, we can see that a=-16, b=30, and c=4.


t=%28-%2830%29%29%2F%282%28-16%29%29 Plug in a=-16 and b=30.


t=%28-30%29%2F%28-32%29 Multiply 2 and -16 to get -32.


t=15%2F16 Reduce.


So the t-coordinate of the vertex is t=15%2F16.


Now that we know the t-coordinate of the vertex, we can use it to find the h-coordinate of the vertex.


h=-16t%5E2%2B30t%2B4 Start with the given equation.


h=-16%2815%2F16%29%5E2%2B30%2815%2F16%29%2B4 Plug in t=15%2F16.


h=-16%28225%2F256%29%2B30%2815%2F16%29%2B4 Square 15%2F16 to get 225%2F256.


h=-225%2F16%2B30%2815%2F16%29%2B4 Multiply -16 and 225%2F256 to get -225%2F16.


h=-225%2F16%2B225%2F8%2B4 Multiply 30 and 15%2F16 to get 225%2F8.


h=289%2F16 Combine like terms.


So the h-coordinate of the vertex is h=289%2F16.


So the vertex is .


This means that the max height is h=289%2F16 which is h=18.0625 feet.