This is a question that is supposed to help my understanding of the second derivative test, but Im not sure how it does, or how to do this.

f(x,y) = a(x^2) + b(xy) + c(y^2)

by completing the square, show that if a/=0 then,

f(x,y) = a(x^2) + b(xy) + c(Y^2) = a[(x + yb/2a)^2 + (y^2)(4ac-b^2)/(4a^2)]