If $f(t) = a_0 + a_1 t + a_2 t^2+\mathcal O(t^3)$, what does the condition $|a_1|/|a_2| > 1$ signify geometrically / analytically?

Question

Let $f:\mathbb R \to \mathbb R$ be a function which is twice continuously differentiable in a neighborhood of zero, with Maclaurin expansion $f(t) = a_0 + a_1 t + a_2 t^2+\mathcal O(t^3)$.

Question. Is the ratio $\zeta:=|a_1|/|a_2|$ attributed any particular meaning in the literature ? What does $\zeta>1$ signify ?