Quadratic polynomial

In mathematics, a quadratic function of a single variable is a function of the form $${\displaystyle f(x)=ax^{2}+bx+c}$$ with ⁠${\displaystyle a\neq 0}$⁠, where ⁠${\displaystyle x}$⁠ is its variable, and ⁠${\displaystyle a}$⁠, ⁠${\displaystyle b}$⁠, and ⁠${\displaystyle c}$⁠ are coefficients. The expression⁠${\displaystyle \textstyle ax^{2}+bx+c}$⁠, especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two. In elementary mathematics a polynomial and its associated polynomial function are rarely distinguished and the terms quadratic function and quadratic polynomial are nearly synonymous and often abbreviated as quadratic.