What is the minimum value of the expression \(x^2+y^2+2x-4y+8\) for real \(x \) and \(y\)?
I can't figure it out help PLEASE.
Thanks in advance.
x^2 + y^2 + 2x - 4y - 8 complete the square on x and y
x^2 +2x + 1 + y^2 - 4y + 4 - 1 - 4 factor
(x + 1)^2 + (y - 2)^2 - 5
The minimum value of -5 will be achieved when x = -1 and y = 2