My professor recently gave me an outline of a correspondence of the following sort: Let $K$ be a field with $\operatorname{char}{K} \neq 2$. Then, there is a correspondence $$ \{ (V,Q) : 2\text{-dim non-degenerate quadratic module} \} \cong \{(L/K, \mathrm{disc}) : L/K \text{ quadratic étale algebra, }\mathrm{disc} \in K^{\times}/N_{L/K}L^{\times} \}$$ up to isomorphism. (There may be some mistakes here but those would be entirely due to me.)
I think that this is an extremely cool result! I would also expect it to be quite fundamental. However, when I tried googling this, I surprisingly found almost no references. My professor also didn't have a reference of the top of his head.
Therefore, I want to ask for references regarding this result.
This might be classified as shameless advertising but this statement can be found in a talk of mine and the proof is sketched on the last two slides.