Mathematics - Quadratic (function|polynomial of degree 2)

In mathematics,

• a polynomial of degree 2,

is a polynomial function in one or more variables in which the highest-degree term is of the second degree.

Quadratus is the Latin word for square.

3 - Type

3.1 - Univariate

Single variable

$f(x)=ax^2+bx+c,\quad a \ne 0$

In elementary algebra, such polynomials often arise in the form of a quadratic equation $ax^2 + bx + c = 0$. The solutions to this equation are called the roots of the quadratic polynomial, and may be found through:

• factorization,
• completing the square,
• graphing,
• Newton's method,
• or through the use of the quadratic formula.

Each quadratic polynomial has an associated quadratic function, whose graph is a parabola.

3.2 - Bivariate

The bivariate case in terms of variables x and y has the form

$f(x,y) = a x^2 + by^2 + cx y+ d x+ ey + f \,\!$