Quadratic function

A quadratic graph with two real answers and no complex answers. Other quadratic graph have no real answers and 2 complex answers.

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 $$f(x)=ax^{2}+bx+c$$ where $a$, $b$ and $c$ are all constants and $a\neq 0$.

When such a function gets plotted on a graph where $f(x)=y$, 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 $x$-axis.

Properties

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

The derivative of a quadratic function is a linear function.

Etymology

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