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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) : Mathematics, Symbolic Computation

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# Vertex Form of a Quadratic

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## Calculate the vertex form

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

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?

Consider 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 $$p(x) = k x^n + c$$

This form is called depressed polynomial.