I don’t want folks thinking I’m claiming a monopoly on the mathematics-glossary front. HowardAt58 is happy to explain words too. Here he talks about one of the definitions of “vertex”, in this case the one that relates to parabolas and other polynomial curves. As a bonus, there’s osculating circles.

Here are some definitions of the vertex of a parabola.

One is complete garbage, one is correct though put rather chattily.

The rest are not definitions, though very popular (this is just a selection). But they are true statements

Mathwarehouse: The vertex of a parabola is the highest or lowest point, also known as the maximum or minimum of a

parabola.

Mathopenref: A parabola is the shape defined by a quadratic equation. The vertex is the peak in the curve as shown on

the right. The peak will be pointing either downwards or upwards depending on the sign of the x^{2} term.

Virtualnerd: Each quadratic equation has either a maximum or minimum, but did you that this point has a special name?

In a quadratic equation, this point is called the vertex!

Mathwords: Vertex of a Parabola: The point at which a parabola makes its sharpest turn.

Purplemath: The…

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Interesting use of the word vertex!

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Is it unfamiliar to you? I’d thought it was a common term, but I might be misjudging its universality. There are dialects in mathematics as in all things.

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In Singapore we usually call it the minimum point / maximum point or turning point

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Oh, I have seen “turning point” used occasionally. And it is a minimum or maximum point, of course, unless the parabola’s been rotated. I remember being tasked with working out rotations of curves in high school, although not since then.

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