Quadratic ○꠹ Entries

↩ 🔵 🔵 🔵

---

Primary

၊၊||၊|။

Quadratic ○꠹｜Definition｜1st｜20251119205401-00-⌔

Quadratic function - Wikipedia

Quadratic function

In mathematics, a quadratic function of a single variable is a function of the form¹

$f(x)=a{x}^2+bx+c$

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

🖼️ ➺

The graph of a real single-variable quadratic function is a parabola. If a quadratic function is equated with zero, then the result is a quadratic equation. The solutions of a quadratic equation are the zeros (or roots) of the corresponding quadratic function, of which there can be two, one, or zero. The solutions are described by the quadratic formula.

A quadratic polynomial or quadratic function can involve more than one variable. For example, a two-variable quadratic function of variables ⁠ $x$ ⁠ and ⁠ $y$ ⁠ has the form

• ✤ $f(x,y)=a{x}^2+bxy+c{y}^2+dx+ey+f,$

with at least one of ⁠ $a$ ⁠, ⁠ $b$ ⁠, and ⁠ $c$ ⁠ not equal to zero. In general the zeros of such a quadratic function describe a conic section (a circle or other ellipse, a parabola, or a hyperbola) in the ⁠ $x$ ⁠ – ⁠ $y$ ⁠ plane. A quadratic function can have an arbitrarily large number of variables. The set of its zero form a quadric, which is a surface in the case of three variables and a hypersurface in general case.

Printed 2026-06-28.

(echo:: @ ᯤ)

Footnotes

1. Weisstein, Eric Wolfgang. “Quadratic Equation”. MathWorld. Retrieved 2013-01-06. ↩

Link to original

Secondary

• • •

---