Quadratic function

Quadratic functions are functions that contains an expression where its degree (the highest exponent it has) is 2, which means that it is quadratic:

$f(x)=ax^{2}+bx+c$

Etymology

The word quadratic comes from the Latin word quadrātum ("square"). This is because of the presence of a number that is to be multiplied to itself ( $x\times x=x^{2}$ ) like how the area of a square is its length multiplied to itself.

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Polynomials and polynomial functions
By degree	Zero polynomial (degree undefined or −1 or −∞) Constant function (0) Linear function (1) Linear equation Quadratic function (2) Quadratic equation Cubic function (3) Cubic equation Quartic function (4) Quartic equation Quintic function (5) Sextic equation (6) Septic equation (7)
By properties	Univariate Bivariate Multivariate Monomial Binomial Trinomial Irreducible Square-free Homogeneous Quasi-homogeneous
Tools and algorithms	Factorization Greatest common divisor Division Horner's method of evaluation Resultant Discriminant Gröbner basis