document.write( "Question 1000563: A function of two variables is defined as f(x.y)=x^2+y^2+4x-6y+7. What is the minimum value of this function? \n" ); document.write( "

Algebra.Com's Answer #617973 by KMST(5328) $\"\"$ $\"About$

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$\"f%28x%2Cy%29=x%5E2%2By%5E2%2B4x-6y%2B7\"$
\n" ); document.write( " $\"f%28x%2Cy%29=x%5E2%2B4x%2By%5E2-6y%2B7\"$
\n" ); document.write( " $\"f%28x%2Cy%29=x%5E2%2B4x%2B4-4%2By%5E2-6y%2B9-9%2B7\"$
\n" ); document.write( " $\"f%28x%2Cy%29=%28x%5E2%2B4x%2B4%29-4%2B%28y%5E2-6y%2B9%29-9%2B7\"$
\n" ); document.write( " $\"f%28x%2Cy%29=%28x%2B2%29%5E2-4%2B%28y-3%29%5E2-9%2B7\"$
\n" ); document.write( " $\"f%28x%2Cy%29=%28x%2B2%29%5E2%2B%28y-3%29%5E2-6\"$
\n" ); document.write( "Since $\"system%28%28x%2B2%29%5E2%3E=0%2C%22and%22%2C%28y-3%29%5E2%3E=0%29\"$ for all values of $\"x\"$ and $\"y\"$ ,
\n" ); document.write( " $\"f%28x%2Cy%29=%28x%2B2%29%5E2%2B%28y-3%29%5E2-6%3E=-6\"$ for all values of $\"x\"$ and $\"y\"$ ,
\n" ); document.write( "so the minimum value is $\"highlight%28-6%29\"$ . \n" ); document.write( "

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