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.
Vertex Form of a Quadratic - dCode
Tag(s) : Symbolic Computation
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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.
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 $
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).
dCode can generalize the approach to degrees $ n $ superior to $ 2 $ by removing the term of degree $ n-1 $ using appropriate factors.
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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