SOLUTION: I just can't get the following problem from my Algebra book: A rocket is launched from atop a 77-foot cliff with an initial velocity of 82 feet per second. The height of the rocke

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Question 38358: I just can't get the following problem from my Algebra book:
A rocket is launched from atop a 77-foot cliff with an initial velocity of 82 feet per second. The height of the rocket t seconds after launch is given by the equation h=-16t^2+82t+77. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest tenth of a second.

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
h=-16t%5E2%2B82t%2B77
Use quadratic formula to determine the zeros.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B82x%2B77+=+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=%2882%29%5E2-4%2A-16%2A77=11652.

Discriminant d=11652 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-82%2B-sqrt%28+11652+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2882%29%2Bsqrt%28+11652+%29%29%2F2%5C-16+=+-0.810763442128409
x%5B2%5D+=+%28-%2882%29-sqrt%28+11652+%29%29%2F2%5C-16+=+5.93576344212841

Quadratic expression -16x%5E2%2B82x%2B77 can be factored:
-16x%5E2%2B82x%2B77+=+-16%28x--0.810763442128409%29%2A%28x-5.93576344212841%29
Again, the answer is: -0.810763442128409, 5.93576344212841. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B82%2Ax%2B77+%29

Since the time can not be negative, the answer is about 5.9 seconds.