SOLUTION: Can I please have help with this, thank you! A football is kicked straight up into the air. Its height above the ground is approximated by the relation y=25x-5x^2, where y is the

Algebra ->  Linear-equations -> SOLUTION: Can I please have help with this, thank you! A football is kicked straight up into the air. Its height above the ground is approximated by the relation y=25x-5x^2, where y is the       Log On


   

Question 1195104: Can I please have help with this, thank you! A football is kicked straight up into the air. Its height above the ground is approximated by the relation y=25x-5x^2, where y is the height of the ball in meters and x is the time in seconds. There are two times when the football is 27.5m in the air, on the way up and on the way down. Joe realizes that using the equation y=27.5, he can determine the two times the ball is 27.5 meters in the air. Algebraically or graphically determine these two times?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A football is kicked straight up into the air. Its height above the ground is approximated by the relation y=25x-5x^2, where y is the height of the ball in meters and x is the time in seconds. There are two times when the football is 27.5m in the air, on the way up and on the way down. Joe realizes that using the equation y=27.5, he can determine the two times the ball is 27.5 meters in the air. Algebraically or graphically determine these two times?
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y=25x-5x^2 = 27.5
5x-x^2 = 5.5
-x^2 + 5x - 5.5 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B5x%2B-5.5+=+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=%285%29%5E2-4%2A-1%2A-5.5=3.

Discriminant d=3 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+3+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+3+%29%29%2F2%5C-1+=+1.63397459621556
x%5B2%5D+=+%28-%285%29-sqrt%28+3+%29%29%2F2%5C-1+=+3.36602540378444

Quadratic expression -1x%5E2%2B5x%2B-5.5 can be factored:
-1x%5E2%2B5x%2B-5.5+=+%28x-1.63397459621556%29%2A%28x-3.36602540378444%29
Again, the answer is: 1.63397459621556, 3.36602540378444. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B5%2Ax%2B-5.5+%29