---
tag: SJREXDSRK2
kind: concept
name: Quadratic function
aliases: [2nd-degree-function, quadratic-expression, quadratic-functions, quadratic-math, quadratic-polynomial, quadratic-trinomial, second-degree-polynomial, second-order-polynomial, single-variable-quadratic-function, y-ax2-bx-c, y-ax-2-bx-c]
sources:
  - wikipedia: en:187240@r1360283093
    locator: Quadratic function
    note: adopted
    mention: wikipedia://en/187240
    sections: [Summary]
same_as:
  wikidata: Q50695
  wikipedia: Quadratic function
inventory: [E74XDC7KKA]
---

## Summary

Quartic function In mathematics, a **quadratic function** of a single variable is a [[function|0EPAT51DXQ]] of the form

$$f(x)=ax^2+bx+c$$

with $a \ne 0$, where $x$ is its variable, and $a$, $b$, and $c$ are coefficients. The expression $\textstyle ax^2+bx+c$, 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*.