Find the absolute max and min for f(x,y)=x^2+y^2+4x-2y

I'm having a really difficult time trying to solve for the maximum. I also followed these notes for the second problem: http://tutorial.math.lamar.edu/Classes/CalcIII/AbsoluteExtrema.aspx
but i keep getting wrong answers... can someone please explain how to do it? thank you!!!

Question

Find the absolute max and min for f(x,y)=x^2+y^2+4x-2y

I'm having a really difficult time trying to solve for the maximum. I also followed these notes for the second problem: http://tutorial.math.lamar.edu/Classes/CalcIII/AbsoluteExtrema.aspx
but i keep getting wrong answers... can someone please explain how to do it? thank you!!!

nikvist · Answer

$$f(x,y)=x^2+y^2+4x-2y$$$$f(x,y)=x^2+4x+4+y^2-2y+1-5$$$$f(x,y)=(x+2)^2+(y-1)^2-5$$$$f_{\min}=-5\quad\mbox{for}\quad (-2,1)$$$$\mbox{absolute max. doesn't exist}$$