En matemáticas, una función cuadrática de una variable es una función polinómica definida por: con . También se da el caso que se le llame Trinomio cuadrático. También se denomina función cuadrática a funciones definidas por polinomios cuadráticos de más de una variable, como por ejemplo: En este caso el conjunto de puntos que resultan al igualar el polinomio a cero representan lugares geométricos que siempre es posible reducir a una de las formas: Que corresponden a tres tipos de secciones cónicas (elipse, hipérbola y parábola).

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In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree. For example, a quadratic function in three variables x, y, and z contains exclusively terms x2, y2, z2, xy, xz, yz, x, y, z, and a constant: with at least one of the coefficients a, b, c, d, e, or f of the second-degree terms being non-zero. A univariate (single-variable) quadratic function has the form in the single variable x. The graph of a univariate quadratic function is a parabola whose axis of symmetry is parallel to the y-axis, as shown at right. If the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the univariate equation are called the roots of the univariate function. The bivariate case in terms of variables x and y has the form with at least one of a, b, c not equal to zero, and an equation setting this function equal to zero gives rise to a conic section (a circle or other ellipse, a parabola, or a hyperbola). In general there can be an arbitrarily large number of variables, in which case the resulting surface is called a quadric, but the highest degree term must be of degree 2, such as x2, xy, yz, etc.

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