Quadratic function

Definition

A quadratic function is a function of the form:

$x\mapsto a{x}^2+bx+c$

where $a,b,c$ are real numbers and $a\ne 0$. In other words, a quadratic function is a polynomial function of degree two.

Key invariants

The discriminant of a quadratic function is the quantity $b^2-4ac$. The sign of the discriminant determines the nature of the factors and zeros of the quadratic function.