About
In mathematics,
- 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.
Quadratus is the Latin word for square.
Articles Related
Type
Univariate
Single variable
<math>f(x)=ax^2+bx+c,\quad a \ne 0</math>
In elementary algebra, such polynomials often arise in the form of a quadratic equation <math>ax^2 + bx + c = 0</math> . 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.
Bivariate
The bivariate case in terms of variables x and y has the form
<math> f(x,y) = a x^2 + by^2 + cx y+ d x+ ey + f \,\!</math>
Formula / Solution
The quadratic formula <MATH> x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\ \ </MATH> expresses the solution of the quadratic equation <MATH>ax^2 + bx + c = 0</MATH>
The symbol <math>\pm</math> expresses the fact that there is two soluctions (ie two root).
Plot
Example: Plot of <math>0.5 (x-1) (x-4)</math> A quadratic function with roots x = 1 and x = 4.