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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 (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.

### 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

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