SOLUTION: The height h in feet of an object after t seconds is given by the function h=-16t^2+40t+6. How long will it take the object to hit the ground? Round your answer to the nearest tho

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Question 60816: The height h in feet of an object after t seconds is given by the function
h=-16t^2+40t+6. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
Thanks!
CH
Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
It hits when h=0, so:
-16t%5E2%2B40t%2B6=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -16t%5E2%2B40t%2B6+=+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=%2840%29%5E2-4%2A-16%2A6=1984.

Discriminant d=1984 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-40%2B-sqrt%28+1984+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2840%29%2Bsqrt%28+1984+%29%29%2F2%5C-16+=+-0.141941090707505
t%5B2%5D+=+%28-%2840%29-sqrt%28+1984+%29%29%2F2%5C-16+=+2.64194109070751

Quadratic expression -16t%5E2%2B40t%2B6 can be factored:
-16t%5E2%2B40t%2B6+=+-16%28t--0.141941090707505%29%2A%28t-2.64194109070751%29
Again, the answer is: -0.141941090707505, 2.64194109070751. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B40%2Ax%2B6+%29

highlight%28t=2.462%29