Question 1000563
{{{f(x,y)=x^2+y^2+4x-6y+7}}}
{{{f(x,y)=x^2+4x+y^2-6y+7}}}
{{{f(x,y)=x^2+4x+4-4+y^2-6y+9-9+7}}}
{{{f(x,y)=(x^2+4x+4)-4+(y^2-6y+9)-9+7}}}
{{{f(x,y)=(x+2)^2-4+(y-3)^2-9+7}}}
{{{f(x,y)=(x+2)^2+(y-3)^2-6}}}
Since {{{system((x+2)^2>=0,"and",(y-3)^2>=0)}}} for all values of {{{x}}} and {{{y}}} ,
{{{f(x,y)=(x+2)^2+(y-3)^2-6>=-6}}}  for all values of {{{x}}} and {{{y}}} ,
so the minimum value is {{{highlight(-6)}}} .