Quadratic function

Polynomial function of degree two

In mathematics, a quadratic function of a single variable is a function of the form f ( x) = a x 2 + b x + c {\displaystyle f(x)=ax^{2}+bx+c} with ⁠ a ≠ 0 {\displaystyle a\neq 0} ⁠, where ⁠ x {\displaystyle x} ⁠ is its variable, and ⁠ a {\displaystyle a} ⁠, ⁠ b {\displaystyle b} ⁠, and ⁠ c {\displaystyle c} ⁠ are coefficients. The expression ⁠ a x 2 + b x + c {\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.

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