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The graph of a real-valued quadratic function of a real variable x, is a parabola.

A quadratic equation is a polynomial equation of degree two. The general form is

$a{x}^2+bx+c=0,$

where a ≠ 0 (if a = 0, then the equation becomes a linear equation). The letters a, b, and c are called coefficients: the quadratic coefficient a is the coefficient of x², the linear coefficient b is the coefficient of x, and c is the constant coefficient, also called the free term.

Quadratic equations are called quadratic because quadratus is Latin for "square"; in the leading term the variable is squared.

A quadratic equation has two (not necessarily distinct) solutions, which may be real or complex, given by the quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a},$

These solutions are roots of the corresponding quadratic function

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

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Image credit: Enoch Lau

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