document.write( "Question 386406: range of y(x-x^2)=9+x^2
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Algebra.Com's Answer #273180 by robertb(5830) $\"\"$ $\"About$

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$\"y%28x-x%5E2%29=9%2Bx%5E2\"$ . Solve for x in terms of y:
\n" ); document.write( " $\"0+=+%281%2By%29x%5E2+-+yx+%2B+9\"$ ;
\n" ); document.write( " $\"x+=+%28y+%2B-+sqrt%28+y%5E2-4%2A%281%2By%29%2A9+%29%29%2F%282%2A%281%2By%29%29+\"$ .
\n" ); document.write( "The discriminant in this case has to be non-negative.
\n" ); document.write( " $\"y%5E2-4%2A%281%2By%29%2A9+%3E=0\"$ , or $\"y%5E2+-+36y+-+36+%3E=+0\"$ .
\n" ); document.write( "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 [ $\"18+%2B+6sqrt%2810%29\"$ , $\"infinity\"$ ).
\n" ); document.write( "This is also the range of the given function. \n" ); document.write( "

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