Unless you take every spring in the Universe to have the same spring constant (nonsense), k must also be treated as a variable. The energy relation for an individual spring is a quadratic form, but the energy relation for all springs is either a cubic form or a set of quadratic forms (or a bijection from the real line to the set of unary quadratic forms, if you want to be really technical and boring).
f(x) = a * x is an example of a function of x which only becomes a function when a value is assigned to the variable 'a'. In other words, it is a type of function.
>Indeed it is, but it's commonly accepted in mathematics to use it as a function of one variable (x), with a parameter a.
In introductory calculus, sure; in those areas of mathematics where the term 'quadratic form' is actually used, things have to be defined more precisely.
Ah, I think I see your point. You would be happier with E = 1/2k x^2 is a family of quadratic forms, indexed by the real number k, I guess. A bit nitpicky to me (as long as k != 0), but fair.
f(x) = a * x is an example of a function of x which only becomes a function when a value is assigned to the variable 'a'. In other words, it is a type of function.
>Indeed it is, but it's commonly accepted in mathematics to use it as a function of one variable (x), with a parameter a.
In introductory calculus, sure; in those areas of mathematics where the term 'quadratic form' is actually used, things have to be defined more precisely.