# Quadratic function

In algebra, a **quadratic function**, a **quadratic polynomial**, a **polynomial of degree 2**, or simply a **quadratic**, is a polynomial function with one or more variables in which the highest-degree term is of the second degree.

For example, a *univariate* (single-variable) quadratic function has the form[1]

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).

A quadratic function in three variables *x*, *y,* and *z* contains exclusively terms *x*^{2}, *y*^{2}, *z*^{2}, *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.

In general there can be an arbitrarily large number of variables, in which case the resulting surface of setting a quadratic function to zero is called a quadric, but the highest degree term must be of degree 2, such as *x*^{2}, *xy*, *yz*, etc.