SOLUTION: a ball is tossed int the air from a height of 12ft at 16ft per sec, how long does it take to reach the earth?

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Question 266273: a ball is tossed int the air from a height of 12ft at 16ft per sec, how long does it take to reach the earth?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
h(t) = -16t^2 + 16t + 12
-4t^2 + 4t + 3 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4x%5E2%2B4x%2B3+=+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=%284%29%5E2-4%2A-4%2A3=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+64+%29%29%2F2%5C-4+=+-0.5
x%5B2%5D+=+%28-%284%29-sqrt%28+64+%29%29%2F2%5C-4+=+1.5

Quadratic expression -4x%5E2%2B4x%2B3 can be factored:
-4x%5E2%2B4x%2B3+=+%28x--0.5%29%2A%28x-1.5%29
Again, the answer is: -0.5, 1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B4%2Ax%2B3+%29