You are watching: What is a second degree polynomial

A second-degree polynomial duty in which all the coefficients the the terms with a degree less than 2 space zeros is called a quadratic function.

### Properties

The graph that a second-degree polynomial function has that vertex in ~ the beginning of the Cartesian plane.The zeros the a second-degree polynomial function are given by the complying with :If (B2 – 4AC) ≥ 0, the zeros are genuine numbers: \(x_1 = \frac−\textrmB\space + \space \sqrt\textrmB^2 − 4\textrmAC2\textrmA\) and \(x_2 = \frac−\textrmB\space −\space \sqrt \textrmB^2 − 4\textrmAC2\textrmA\);If the role is that the form*f*(

*x*) = A\(x^2\) + B\(x\), the zeros are : \(x_1\) = 0 and also \(x_2\) = − \(\fracBA\);If the function is of the type

*f*(

*x*) = A\(x^2\) + C, the zeros are : \(x_1\) = \(\sqrt− \fracCA\) and \(x_2\) = − \(\sqrt− \fracCA\), where AC If the duty is that the kind

*f*(

*x*) = A\(x^2\), the zeros are : \(x_1\)= 0 and \(x_2\)= 0.

### Examples

The graphical depiction of a second-degree polynomial function defined through the relationship \(f(x) = x^2\) is a an easy parabola.The graphical representation of a second-degree polynomial role defined through the connection \(f(x) = (x − a)^2\) is a simple parabola analyzed horizontally.The graphical representation of the second-degree polynomial function defined by the connection \(f(x) = x^2 + k\) is a basic parabola translated vertically.See more: What Does The Name Brock Mean Ing, Popularity And Info On Babynames

The graphical depiction of the second-degree polynomial duty defined by the relationship \(f(x) = a(x − h)^2 + k\) is a straightforward parabola interpreted horizontally and also vertically.

This graph illustrates the duty *f* identified by *f*(*x*) = \(\left ( x+3 \right )^2 – 4\)