SOLUTION: 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?

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Question 1026802: 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?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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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?
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Complete the squares in "x" and "y" separately:

x%5E2+%2B+y%5E2+-+4x+%2B+2y = %28x-2%29%5E2+-+4+%2B+%28y-1%29%5E2+-+1 = %28x-2%29%5E2+%2B+%28y-1%29%5E2+-+5.


Now it is clearly seen that the minimal temperature is -5 units.
The other two addends in the right side are non-negative.