Quadratic Equations

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

Published by
Mike Woodhill PhD

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.


Mike Woodhill PhD

As a long time instructor I would like you to benefit from my Step by Step Calculators. You may also schedule a live tutoring session to succeed in your class. 😉

Published by
Mike Woodhill PhD

Recent Posts

  • uncategorized

LaPlace Transform Calculator

Laplace Transform Calculator Enter your Function in terms t to find any Laplace Transform. How…

11 months ago
  • Parabola

Parabola Graphing Calculator

What is the purpose of the Parabola Graphing Calculator? It allows you to graph Parabolas.…

11 months ago
  • Mike

Contact Mike

For Questions, Bookings, etc : Chat with us. Email us : support@mikescalculator.com Or call us…

11 months ago
  • Tutoring

Schedule Tutoring Session

For Questions, Bookings, etc : Chat with us. Email us : support@mikescalculator.com Or call us…

11 months ago
  • Quadratic Equations

Domain and Range of Parabola

Table of Content (8 min. reading time) 1 - Step by Step Solver: Find the…

11 months ago
  • Algebra

Domain and Range Calculator

What is the Domain and Range? 1) The Domain is defined as the set of…

11 months ago
  • Statistics

What is the Mean in Math?

What does the Mean mean in Math? The Mean in Mathematics is just another word…

11 months ago
  • Statistics

Sample Standard Deviation

What is the Formula for Sample Standard Deviation ? The Formula for the Standard Deviation…

11 months ago
  • Statistics

Mean Median Mode Range Calculator

How do you find Mean, Median, Mode, Range, Standard Deviation and Variance? Mean = Average…

11 months ago
  • Algebra

Compute Discriminant – to discriminate between Real and Complex Solutions of Quadratic Equation.

What you will learn in this mini lesson You will learn how to find the…

11 months ago
  • Algebra

How to Factor Quadratic Equation and Solve It.

What you will learn in this mini lesson You will learn how to factor and…

11 months ago
  • Algebra

Standard Form of Quadratic Function

What you need to know about Standard Form of a Quadratic Function The Quadratic Equation…

11 months ago
  • Vertex

Vertex Form in 5 Minutes (Formulas, Solvers, Examples)

What is Vertex Form of a Quadratic Equation? The Vertex Form is f(x) = a(x-h)²+k…

11 months ago
  • Algebra

Solve A Quadratic Equation by Completing the Square

What you will learn in this mini lesson You will learn how to solve Quadratic…

11 months ago
  • Algebra

STANDARD TO VERTEX FORM CALCULATOR

Table of Content (8 min. reading time) 1 - Step by Step Solver: Find the…

11 months ago
  • Vertex Form of a Parabola

VERTEX TO STANDARD FORM CALCULATOR

How to convert from Vertex to Standard Form? The Vertex Form of a Parabola is…

11 months ago
  • Statistics

Standard Deviation to Variance

Standard Deviation to Variance Calculator What is the difference between Variance and Standard Deviation? Both…

1 year ago
  • Algebra

Quadratic Form Calculator

What you will learn in this mini lesson You will learn how to solve Quadratic…

2 years ago
  • Python

Python Random Number Generator

How to generate Random Numbers using Python's Random Number Generator. 1) Let's start with an…

2 years ago