SOLUTION: A function of two variables is defined as f(x.y)=x^2+y^2+4x-6y+7. What is the minimum value of this function?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A function of two variables is defined as f(x.y)=x^2+y^2+4x-6y+7. What is the minimum value of this function?       Log On


   

Question 1000563: A function of two variables is defined as f(x.y)=x^2+y^2+4x-6y+7. What is the minimum value of this function?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%2Cy%29=x%5E2%2By%5E2%2B4x-6y%2B7
f%28x%2Cy%29=x%5E2%2B4x%2By%5E2-6y%2B7
f%28x%2Cy%29=x%5E2%2B4x%2B4-4%2By%5E2-6y%2B9-9%2B7
f%28x%2Cy%29=%28x%5E2%2B4x%2B4%29-4%2B%28y%5E2-6y%2B9%29-9%2B7
f%28x%2Cy%29=%28x%2B2%29%5E2-4%2B%28y-3%29%5E2-9%2B7
f%28x%2Cy%29=%28x%2B2%29%5E2%2B%28y-3%29%5E2-6
Since system%28%28x%2B2%29%5E2%3E=0%2C%22and%22%2C%28y-3%29%5E2%3E=0%29 for all values of x and y ,
f%28x%2Cy%29=%28x%2B2%29%5E2%2B%28y-3%29%5E2-6%3E=-6 for all values of x and y ,
so the minimum value is highlight%28-6%29 .