confused about nomenclature

It seems there are three generally recognized forms of quadratic functions:

1. ax² + bx + c = 0

2. y = a(x - h)² + k

3. 4p(y - k) = (x - h)²

I've seen (1) called the standard form or the general form

(2) seems always to be called the vertex form

(3) seems to be called the standard form, the general form, or the factored form.

What is the most consistent, correct way to refer to these equation forms? Isn't there some "official" nomenclature?

Thanks for any help or suggestions.