SOLUTION: h=-9.8t^2+15t+160

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Question 549311: h=-9.8t^2+15t+160
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -9.8t%5E2%2B15t%2B160+=+0) has the following solutons:

t%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=%2815%29%5E2-4%2A-9.8%2A160=6497.

Discriminant d=6497 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-15%2B-sqrt%28+6497+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2815%29%2Bsqrt%28+6497+%29%29%2F2%5C-9.8+=+-3.34714133293605
t%5B2%5D+=+%28-%2815%29-sqrt%28+6497+%29%29%2F2%5C-9.8+=+4.87775357783401

Quadratic expression -9.8t%5E2%2B15t%2B160 can be factored:
-9.8t%5E2%2B15t%2B160+=+-9.8%28t--3.34714133293605%29%2A%28t-4.87775357783401%29
Again, the answer is: -3.34714133293605, 4.87775357783401. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-9.8%2Ax%5E2%2B15%2Ax%2B160+%29