In elementary algebra, a quadratic function is a function containing a quadratic expression, a polynomial where the degree (the highest exponent it has) is 2. The single-variable standard form of a quadratic function isː 👁 {\displaystyle f(x)=ax^{2}+bx+c}
where 👁 {\displaystyle a}
, 👁 {\displaystyle b}
and 👁 {\displaystyle c}
are all constants and 👁 {\displaystyle a\neq 0}
.

When such a function gets plotted on a graph where 👁 {\displaystyle f(x)=y}
, a curve that extends infinitely called a parabola will appear.

When a quadratic function is set to some value, it makes a quadratic equation. When the value is zero, the equation is said to be in standard form, and its solutions are the places where the function crosses the 👁 {\displaystyle x}
-axis.

Quadratic functions have a single extremum. This point, which is a minimum if 👁 {\displaystyle a>0}
and a maximum if 👁 {\displaystyle a<0}
, is called the vertex of the parabola.

The derivative of a quadratic function is a linear function.

The word quadratic comes from the Latin word quadrātum ("square"). The highest degree term, 👁 {\displaystyle x^{2}}
, is the area of a square with side length 👁 {\displaystyle x}
. The word "quadratic" is applied to many things in mathematics that involve this 👁 {\displaystyle x^{2}}
term. A similar etymology is shared with cubic functions, which have an 👁 {\displaystyle x^{3}}
term that is the volume of the cube of side length 👁 {\displaystyle x}
. Higher degrees like quartic functions and up take their name from the degree directly using numeric prefixes.