Quadratic function

In elementary algebra, a quadratic function is a function containing a quadratic expression, a polynomial where the degree (the highest exponent it has) is 2. The single-variable standard form of a quadratic function isː

where ,  and  are all constants and .

When such a function gets plotted on a graph where , a curve that extends infinitely called a parabola will appear.

When a quadratic function is set to some value, it makes a quadratic equation. When the value is zero, the equation is said to be in standard form, and its solutions are the places where the function crosses the -axis.

 Properties 
Quadratic functions have a single extremum. This point, which is a minimum if  and a maximum if , is called the vertex of the parabola.

The derivative of a quadratic function is a linear function. 

 Etymology 
The word quadratic comes from the Latin word quadrātum ("square"). The highest degree term, , is the area of a square with side length . The word "quadratic" is applied to many things in mathematics that involve this  term. A similar etymology is shared with cubic functions, which have an  term that is the volume of the cube of side length . Higher degrees like quartic functions and up take their name from the degree directly using numeric prefixes.

Category:Algebra