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!

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.

Answers to Questions

How to find the vertex form a quadratic polynomial?

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 \( (x-2)^2+2 \) with the quadratic to vertex form calculator

dCode 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 source code of the script Vertex Form of a Quadratic online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. To download the online Vertex Form of a Quadratic script for offline use on PC, iPhone or Android, ask for price quote on contact page !