SOLUTION: Please help s(t) = -16t^2 + 32t Graph this function for 0 < or = t which is < or = to 2. Also, what is the maximum height reached by the ball. Thanks, Paul

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Question 23310: Please help
s(t) = -16t^2 + 32t Graph this function for 0 < or = t which is < or = to 2.
Also, what is the maximum height reached by the ball.
Thanks,
Paul
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B32x%2B0+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2832%29%5E2-4%2A-16%2A0=1024.

Discriminant d=1024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+1024+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+1024+%29%29%2F2%5C-16+=+0
x%5B2%5D+=+%28-%2832%29-sqrt%28+1024+%29%29%2F2%5C-16+=+2

Quadratic expression -16x%5E2%2B32x%2B0 can be factored:
-16x%5E2%2B32x%2B0+=+-16%28x-0%29%2A%28x-2%29
Again, the answer is: 0, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B32%2Ax%2B0+%29

a=-16, b=32, c=0
The max or min is found at t=-b/2a = 32/32=1
Get the correspond "s" value by plugging
in t=1.
Cheers,
Stan H.