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Tool to find the vertex form of a polynomial. The vertex form a quadratic polynomial is an expressed form where the variable x appears only once.

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Vertex Form of a Quadratic -

Tag(s) : Symbolic Computation

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# Vertex Form of a Quadratic

## Standard Form Calculator (expanded)

Tool to find the vertex form of a polynomial. The vertex form a quadratic polynomial is an expressed form where the variable x appears only once.

### What is the vertex form a quadratic polynomial? (Definition)

A quadratic polynomial $p(x)=ax^2+bx+c$ (with $a$ not null) can be written in a canonic form $p(x)=a(x−α)^2+β$.

Example: The polynomial of order 2 $x^2-4x+6$ can be written $(x-2)^2+2$

### How to find the vertex form a quadratic polynomial?

The principle is to factorize the second degree coefficient to remove the first degree coefficient.

dCode converter to vertex form calculator uses multiple methods to find the canonical form of a polynomial function of second degree, including the completion of the square or Tschirnhaus transformation (both using mathematical expression factorisation).

### How to find the vertex form of a nth degree polynomial?

dCode can generalize the approach to degrees $n$ superior to $2$ by removing the term of degree $n-1$

### What is the Tschirnhaus method?

For a polynomial $$p(x) = a_n x^n + a_{n-1} x^{n-1} + a_{n-2} x^{n-2} + \cdots + a_1 x + a_0$$ the Tschirnhaus transformation consists in writing it as $$p(x) = k x^n + c$$

The result is called depressed polynomial and the technique is polynomial depression.

## Source code

dCode retains ownership of the online 'Vertex Form of a Quadratic' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Vertex Form of a Quadratic download for offline use on PC, tablet, iPhone or Android !

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