How to convert standard form to vertex form by completing the square?

We will use the concepts of factorization of polynomial and quadratic equations to convert standard form to vertex form by completing the square.

Explanation :

Quadratic equation in a general form can be written as y = ax²+bx+c

Now let's see how we will use the concepts of factorization of polynomial and quadratic equation in general form to convert standard form to vertex form by completing the square.

Step 1: Isolate x on one side of the equation.

⇒ y = x² + 12x + 32

⇒ y - 32 = x² + 12x

Step 2: Use completing the square method as shown below.

⇒ y - 32 + 36 = x² + 12x + 36  [ adding 36 on both sides to make RHS as a perfect square ]

⇒ y + 4 = (x + 6)²

⇒ y = (x + 6)² - 4 

Hence, the standard vertex form is y = (x + 6)² - 4 

These are the ways to convert standard form to vertex form by completing the square.