SOLUTION: A ball is projected into the air. Its height at time t is given by the equation h = -16t^2 + 60x +1. When will the height be 8 feet?

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Question 291689: A ball is projected into the air. Its height at time t is given by the equation h = -16t^2 + 60x +1. When will the height be 8 feet?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A ball is projected into the air. Its height at time t is given by the equation h = -16t^2 + 60x +1. When will the height be 8 feet?
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When h = 8
8 = -16t^2 + 60t + 1 (I think you meant 60t, not 60x)
-16t^ + 60t - 7 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B60x%2B-7+=+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=%2860%29%5E2-4%2A-16%2A-7=3152.

Discriminant d=3152 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-60%2B-sqrt%28+3152+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2860%29%2Bsqrt%28+3152+%29%29%2F2%5C-16+=+0.120541394047725
x%5B2%5D+=+%28-%2860%29-sqrt%28+3152+%29%29%2F2%5C-16+=+3.62945860595227

Quadratic expression -16x%5E2%2B60x%2B-7 can be factored:
-16x%5E2%2B60x%2B-7+=+%28x-0.120541394047725%29%2A%28x-3.62945860595227%29
Again, the answer is: 0.120541394047725, 3.62945860595227. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B60%2Ax%2B-7+%29

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x1 and x2 are the values of t.
There are 2 of them, 8 feet going up, and 8 feet coming back down.