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?

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) (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:

 =  = .


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

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