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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.

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: \( x^2-4x+6 = (x-2)^2+2 \)

dCode uses multiple methods to find the canonical form of a polynomial function of degree 2, including the completion of the square or Tschirnhaus transformation.

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.

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Source code

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