My understanding is that it is related to the notion of "quadrature", meaning to turn into a square (four-sided). For if x represents a linear segment then x^2 should be represented by a quadrangular region. I'm sure others will provide more detail and correct me if I'm wrong.
> Today I had a student in my college algebra class ask me why > "Quadratic Equations" are so named. If we have a polynomial of > degree 3 set equal to zero, we call it a cubic equation and that > makes sense to these students. However, this particular student is > curious because she sees "Q-U-A-D" in quadratic and thinks of four, > yet the polynomial in such an equation is only of degree 2. I've > never encountered this question before and I was at a loss for an > explanation. Does anyone know the origin of the term "quadratic > equation"? I would be very grateful to receive an answer. > > > Thank you in advance. > > Jeff Darrow > Idaho State University > >