The word "quad" generally means 4. Quadratics don't have 4 of anything. Can anyone explain where the name comes from?

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Quadrat is the german word for Square. –  anon Sep 14 '10 at 5:34
mathforum.org/library/drmath/view/57456.html gives some history. –  Ｊ. Ｍ. Sep 14 '10 at 5:43
In Dutch, a quadratic equation is called a 'vierkantsvergelijking' - which translates back to 'square equation' (vier = four, kant = side, vergelijking = equation). –  yatima2975 Sep 14 '10 at 10:59
@yatima2975 - I've always learnt it as 'kwadratische vergelijking' (quadratic equation). However, the Dutch word 'kwadraat' is square in English. –  Arda Xi Oct 15 '10 at 14:08

The Latin prefix quadri- is used to indicate the number 4, for example, quadrilateral, quadrant, etc. However, it also very commonly used to denote objects involving the number 2. This is the case because quadratum is the Latin word for square, and since the area of a square of side length $x$ is given by $x^2$, a polynomial equation having exponent two is known as a quadratic ("square-like") equation. By extension, a quadratic surface is a second-order algebraic surface.