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

$ax^2+b x+c=a(x^2+\frac{bx}{a}+\frac{c}{a})\\\\=a[(x+\frac{b}{2a})^2+\frac{c}{a}-(\frac{b}{2a})^2]$

Squared Part is $a(x+\frac{b}{2a})^2$

Number is $a[\frac{c}{a}-(\frac{b}{2a})^2]$

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.