Question

A method used to rearrange a quadratic equation into a squared part and a number. this can allow you to find the vertex of a quadratic or solve a quadratic relatively easily.

Answer 1

Are you looking for the name of the method? If so, it's called completing the square.

Answer 2

Answer with explanation:

Consider the Quadratic Polynomial

`ax^2+b x+c=a(x^2+(bx)/(a)+(c)/(a))\\\\=a[(x+(b)/(2a))^2+(c)/(a)-((b)/(2a))^2]`

Squared Part is
`a(x+(b)/(2a))^2`

Number is
`a[(c)/(a)-((b)/(2a))^2]`

This Method is called Completing the Square.

In this method we ,divide the term containing x by 2,and then reduce it in the form of either (a+b)² or (a-b)².