SOLUTION: y=-2x^2+12x-19

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Question 548103: y=-2x^2+12x-19
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B12x%2B-19+=+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=%2812%29%5E2-4%2A2%2A-19=296.

Discriminant d=296 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+296+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+296+%29%29%2F2%5C2+=+1.30116263352131
x%5B2%5D+=+%28-%2812%29-sqrt%28+296+%29%29%2F2%5C2+=+-7.30116263352131

Quadratic expression 2x%5E2%2B12x%2B-19 can be factored:
2x%5E2%2B12x%2B-19+=+2%28x-1.30116263352131%29%2A%28x--7.30116263352131%29
Again, the answer is: 1.30116263352131, -7.30116263352131. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B12%2Ax%2B-19+%29