Question 54474
1. A baseball hit straight up in the air is at height h feet above the ground, whre h is given by h(t)= 4+50t-16tē, t seconds after being hit. 
A)State a reasonable domain for this function
Maybe 0<=t<=10.  The ball is in the air maybe as long as 10 seconds.
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B)What is the y -intercept? Interpret the y-intercept relative to this situation
To find the y-intercept let t=0.
You get h(0)=4+50*0-16*0^2
h(0)=4 ft.
That means the baseball is four feet off the ground when it is first hit.
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C)When does the baseball hit the ground?
It hits the ground when h(t)=0, that is when it's height is zero.
Solve 4+50t-16t^2=0
t=[-50+-sqrt(50^2-4(-16)(4)]/(-32)
t=[-50+-sqrt(2756)]/(-32)
t=3.2 seconds
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D)When, if ever, is it 30 feet high? 90 feet high?
Solve 30=4+50t-16t^2
Solve 90=4+50t-16t^2
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E)What is the maximum height that the baseball reaches? When does it reach that height?
It reaches the maximum when t=-50/(-32)=1.56 seconds
That is approximately half-way between t=0 and t=3.2

Cheers,
Stan H.