Question: quadratic normalform ?

Let be q(x) some polynomial of degree = 2 in several, n variables x[i],
x to be thought as (row) vector

Can Maple provide the quadratic normalform for q (real resp. complex)?

By this it is meant that q ° f (x) equals one of

  Sum( c[i]*x[i], i=1..n)
  Sum( c[i]*x[i], i=1..n) + 1
  Sum( c[i]*x[i], i=1..n) + x[n+1]

where c[i] in K, K = Reals or Complex (should not matter so much, except
char(K), and square roots have to exist, so Rationals(squareRoots) is fine),
and f: K^n -> K^n is affine ( = bijective and linear + shift vector)?

Once I learned that stuff in Linear Algebra, but it is messy to read
through old scripts, trying to understand and code it in Maple :-(

It is just a question, whether someone has it, so sorry for the rather
short 'definition'. Student[Precalculus][CompleteSquare] does not quite
what I want.