parabola-forms

The 3 Parabola Forms: Standard Form, Vertex Form and Factored Form.

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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
2x2 -12x+16 Factor out 2:
= 2(x2 -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+c
Vertex 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+8
can be rewritten in Vertex Form: 
 y = (x+3)²-1
It 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 is 
 y=a(x-h)²+k
where (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.