I was referring to this lecture http://www.stanford.edu/class/ee364a/videos/video04.html. and he gave an example of a generalized quadratic equation
f(x,y) = x'Ax + 2x'By + y'Cy
The functions is convex if the matrix
A B
B' C
is positive semidefinite and also the matrix C. I didn't get how this is derived and how the function f(x,y) is a generalized quadratic equation