### What you will learn in this mini lesson

You will learn how the 3 different forms of Quadratic Equations and their uses. Our Step by Step Calculators allow you to convert your quadratic equation from one form to another.**Quick Example: Convert from Standard to Factored Form**

2x

^{2}-12x+16 Factor out 2:

= 2(x

^{2}-6x+8)

= 2(x-4)*(x-2) since (-4) + (-2) = -6 and (-4)*(-2)=8

That’s all 😉

# What are the 3 different Forms of Quadratic Equations?

There are 3 different forms of Quadratic Equations:Standard Form:

y = ax²+bx+cVertex Form:

y = a(x-h)²+k(h,k) = Vertex Coordinates.

Factored Form:

y = a(x-r)(x-s)r and s = Zeros of the Parabola.

### Example of the 3 different forms?

Standard Form:

y = x²+6x+8can be rewritten in Vertex Form:

y = (x+3)²-1It tells us that above Parabola has Vertex Coordinates = (3,-1).

The process to convert from Standard Form to Vertex Form is called “Completing the Square”. You can Complete the Square for your quadratic equation here: You can read the details and examples on how to convert here:

/solve-a-quadratic-equation-by-completing-the-square/

Factored Form:

y = (x+4)(x+2)It tells us that above Parabola has Zeros -4 and -2 .

The process to convert from Standard Form to Factored Form can be done here: You can read the details and examples on how to convert here.

Or simply use the head menu when converting between the different Parabola Forms.

### How do I convert from Vertex Form to Standard Form?

The Vertex Form of a Parabola isy=a(x-h)²+kwhere

**(h,k)**are the Vertex Coordinates.

The Standard form of a Parabola is

y=ax²+bx+c

#### Let’s do an easy example first

Let**y=2(x-1)²-5**

we first apply the binomial formula to expand and get

**y=2(x²-2x+1)-5**

Next, we distribute the 2 to get

**y= 2x²-4x+2-5**

With 2-5=-3 we finally arrive at the Standard Form:

**y=2x²-4x-3**

In general, we obtain the Standard Form from the Vertex Form by using these 2 steps:

Given:

**y=a(x-h)²+k**

Step1: (Use Binomial Formula)

**y=a(x²-2hx+h²)+k**

Step2: (Distribute and Combine 2 like terms ah² and k)

**y=ax²-(2ah)x+(ah²+k)**

We created a separate page for you that teaches the Vertex to Standard Form Conversion. It also has a Solver that allows you convert you Vertex Form Equation into Standard Form. Visit our page here.