Search for a tool

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.

Results

Vertex Form of a Quadratic -

Tag(s) : Symbolic Computation

Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Thanks to your feedback and relevant comments, dCode has developed the best 'Vertex Form of a Quadratic' tool, so feel free to write! Thank you!

# Vertex Form of a Quadratic

## Standard Form Calculator (expanded)

### 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 of 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 factorization).

### 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 $n-1$ using appropriate factors.

### 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 'Vertex Form of a Quadratic' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Vertex Form of a Quadratic' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Vertex Form of a Quadratic' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

## Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!