document.write( "Question 1040894: The temperature of a point $(x,y)$ in the plane is given by the expression $x^2 + y^2 - 4x + 2y$. What is the temperature of the coldest point in the plane? \n" ); document.write( "

Algebra.Com's Answer #655805 by Fombitz(32388) $\"\"$ $\"About$

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$\"T=x%5E2%2By%5E2-4x%2B2y\"$
\n" ); document.write( " $\"T=%28x%5E2-4x%29%2B%28y%5E2%2B2y%29\"$
\n" ); document.write( " $\"T=%28x%5E2-4x%2B4%29%2B%28y%5E2%2B2y%2B1%29-4-1\"$
\n" ); document.write( " $\"T=%28x-2%29%5E2%2B%28y%2B1%29%5E2-5\"$
\n" ); document.write( "Since the two quadratic terms can only be non-negative, the minimum T occurs when $\"x-2=0\"$ and $\"y%2B1=0\"$ . The temperature then would be,
\n" ); document.write( " $\"T%5Bmin%5D=-5\"$ at ( $\"2\"$ , $\"-1\"$ )
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