# Quadratic Function

A Quadratic Function is a polynomial function with a function degree of two.

**AKA:**Second-Order Polynomal.**Context:**- It can range from being a Univariate Second-Order Polynomal Function to being a Multivariate Second-Order Polynomal Function.
- It can be referenced by a Quadratic Equation.

**Example(s):**- [math]\displaystyle{ f(x)=ax^2+bx+c, \quad a \ne 0 }[/math].
- [math]\displaystyle{ f(x,y) = a x^2 + by^2 + cx y+ d x+ ey + f, \quad a \ne 0, \quad b \ne 0 }[/math].
- …

**Counter-Example(s):****See:**Quadratically Constrained Quadratic Program, Graph of a Function, Parabola, Root of a Function, Conic Section, Circle, Ellipse, Hyperbola.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/quadratic_function Retrieved:2015-11-7.
- 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*x*^{2}, yz^{2},xy^{2},*,*xz*,*yz*,*x*,*y*,*z*, and a constant: : [math]\displaystyle{ f(x,y,z)=ax^2+by^2+cz^2+dxy+exz+fyz+gx+hy+iz +j, }[/math] 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 : [math]\displaystyle{ f(x)=ax^2+bx+c,\quad a \ne 0 }[/math] 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 : [math]\displaystyle{ f(x,y) = a x^2 + by^2 + cx y+ d x+ ey + f \,\! }[/math] 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*x^{2},*xy*,*yz*, etc.

- In algebra, a