SOLUTION: range of y(x-x^2)=9+x^2

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Question 386406: range of y(x-x^2)=9+x^2
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
y%28x-x%5E2%29=9%2Bx%5E2. Solve for x in terms of y:
0+=+%281%2By%29x%5E2+-+yx+%2B+9;
x+=+%28y+%2B-+sqrt%28+y%5E2-4%2A%281%2By%29%2A9+%29%29%2F%282%2A%281%2By%29%29+ .
The discriminant in this case has to be non-negative.
y%5E2-4%2A%281%2By%29%2A9+%3E=0, or y%5E2+-+36y+-+36+%3E=+0.
By using the quadratic formula to get the critical numbers of this inequality, and picking test numbers, we get the solution to be (-infinity, 18+-+6sqrt%2810%29]U [18+%2B+6sqrt%2810%29, infinity).
This is also the range of the given function.