SOLUTION: I have a question with this word problem. "A toy rocket is launched from ground level. Its distance in feet from the ground in t seconds is given by the formula {{{s(t)=-16t^2+

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Question 682261: I have a question with this word problem.
"A toy rocket is launched from ground level. Its distance in feet from the ground in t seconds is given by the formula s%28t%29=-16t%5E2%2B208t
I need to know when will the rocket be 550ft from the ground?
I already plugged in 550 for s(t) but am unsure of how to proceed further.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!

"A toy rocket is launched from ground level. Its distance in feet from the ground in t seconds is given by the formula s%28t%29=-16t%5E2%2B208t
I need to know when will the rocket be 550ft from the ground?
I already plugged in 550 for s(t) but am unsure of how to proceed further.
.
That is the right approach.
550=-16t%5E2%2B208t
0+=+-16t%5E2%2B208t-550
0+=+16t%5E2-208t%2B550
0+=+8t%5E2-104t%2B275
.
applying the "quadratic formula" yields:
t = {9.31, 3.69}
so, the rocket will be at 550 feet at
3.69 seconds (on the way up)
and again at
9.31 seconds (on the way down)
.
.
Details of quadratic formula follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 8t%5E2%2B-104t%2B275+=+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=%28-104%29%5E2-4%2A8%2A275=2016.

Discriminant d=2016 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--104%2B-sqrt%28+2016+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%28-104%29%2Bsqrt%28+2016+%29%29%2F2%5C8+=+9.30624304008046
t%5B2%5D+=+%28-%28-104%29-sqrt%28+2016+%29%29%2F2%5C8+=+3.69375695991954

Quadratic expression 8t%5E2%2B-104t%2B275 can be factored:
8t%5E2%2B-104t%2B275+=+8%28t-9.30624304008046%29%2A%28t-3.69375695991954%29
Again, the answer is: 9.30624304008046, 3.69375695991954. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-104%2Ax%2B275+%29