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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Vertex Form of a Quadratic
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Calculate the vertex form
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.
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
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