I Like Abstract Stuff; Why Should I Care?

Polynomials make some of the simplest functions around, and quadratic polynomials are the simplest kind of polynomial after a straight line. Wherever you find a reason to use functions—in Algebra, Calculus, and beyond—you'll find quadratics not far behind. When you're being introduced to some new concept, it's comforting to have an old friend along to show you the ropes, instead of some new, scary function that would rather beat you up and take your lunch money.