 Morse Theory by John Milnor

Princeton University Press book; inspected title page dates the edition 1963. Institutional scan: pagine.dm.unipi.it/~a019210/Milnor_Morse%20theory.pdf

Lemma 2.2 gives the exact smooth quadratic normal form and its completion-of-squares proof. Corollary 2.3 gives isolation of nondegenerate critical points and contrasts degenerate examples such as x cubed.