The difference between two quadratics

Take one quadratic and subtract it from the other. Is the result a line? If you graph the difference, the answer is clearly ‘no’—there’s some kind of curve there. Here, we show through a graphical algebraic proof that the difference between two quadratics is indeed a quadratic—and that each coefficient in the result is the difference between the corresponding coefficients in the original quadratics. This is a premonition of an abstract algebraic view, in which polynomials are special kinds of numbers, that can be added, subtracted, and multiplied and divided one from another.