Reading the Vertex (curve) Wikipedia page, the section about cusps and osculation says:
Although a single generic curve will not have any higher-order vertices, they will generically occur within a one-parameter family of curves, at the curve in the family for which two ordinary vertices coalesce to form a higher vertex and then annihilate.
I'm a little confused about what this is implying. Can you perhaps reword it, provide an example, and/or pictures? Especially the last part of the explanation, about forming a higher vertex and then annihilation....
Thank you.