We study the solutions f: G→H of the quadratic functional equation on G, where G and H are groups, H abelian. We show that any solution f is a function on the quotient group [G,[G,G]]. By help of this we find sufficient conditions on G for all solutions to satisfy Kannappan's condition. We use this to derive explicit formulas for the solutions on various groups like, e.g. the (ax+b)-group and GL(n,R).
