Posted on January 8, 2016September 18, 2018 by Kirk Weiler

CC Alg II – The Standard Form of a Parabola – by Sean Finity of Marion CS

Sean Finity of Marion Central Schools sent us a great follow-up lesson to our Unit #6.Lesson #11 – Locus Definition of a Parabola. He introduces the “Standard Form of a Parabola”, i.e.

4p(y-k)=(x-h)^2

You may have never seen this formula before, or perhaps you have. It can be used to generate the formula for a parabola if you know it’s vertex (h,k) and the distance between the vertex and the focus (or equivalently the distance between the vertex and directrix). This is the parameter p.

This formula shows up in one of NYSED’s Common Core Algebra II nonsample-sample questions from last spring.

Sean has put together a great lesson on how to use this formula and shared it with us. Here’s his lesson (with a homework set):

U8D4 General Equation of a Parabola

I created a Desmos interactive graph that allows people to play around with the focus and the directrix and to see how they interact with this formula. Here it is:

The Standard Form of a Parabola – Desmos Activity

I will admit, I’m not the biggest fan of the Standard Form formula, but I really like Sean’s lesson and, given the likelihood of this topic on the exam, I think it is a good one to add in. Again, I can think of very little less “Common Core” than memorizing a formula that doesn’t really link back to the locus definition of a parabola (well, it does, but I don’t know how many kids will appreciate that fact). Notice that this formula is not in the standards nor is it on the NYSED approved formula sheet. But, it sure makes finding the formula of a parabola given its focus and directrix a lot easier.

Thanks Sean!!!

Terms and Conditions

WHY. We are a small, independent publisher founded by a math teacher and his wife. We believe in the value we bring to teachers and schools, and we want to keep doing it. We keep our prices low so all teachers and schools can benefit from our products and services. We ask that you help us in our mission by complying with these Terms & Conditions.

PLEASE, NO SHARING. We know it’s nice to share, but please don’t share your membership content or your login or validation info. Your membership is a Single User License, which means it gives one person – you -- the right to access the membership content (Answer Keys, editable lesson files, pdfs, etc.) but is not meant to be shared.

Please do not copy or share the Answer Keys or other membership content.
Please do not post the Answer Keys or other membership content on a website for others to view. This includes school websites and teacher pages on school websites.
You can make copies of the Answer Keys to hand out to your class, but please collect them when the students are finished with them.
If you are a school, please purchase a license for each teacher/user.

PLEASE RESPECT OUR COPYRIGHT AND TRADE SECRETS. We own the copyright in all the materials we create, and we license certain copyrights in software we use to run our site, manage credentials and create our materials; some of this copyrighted software may be embedded in the materials you download. When you subscribe, we give you permission (a “Single User License”) to use our copyrights and trade secrets and those we license from others, according to our Terms & Conditions. So in addition to agreeing not to copy or share, we ask you:

Please don’t reverse-engineer the software; and please don’t change or delete any authorship, version, property or other metadata.
Please don’t try to hack our validation system, or ask anyone else to try to get around it.
Please don’t put the software, your login information or any of our materials on a network where people other than you can access it
Please don’t copy or modify the software or membership content in any way unless you have purchased editable files;
If you create a modified assignment using a purchased editable file, please credit us as follows on all assignment and answer key pages:

“This assignment is a teacher-modified version of [eMath Title] Copyright © 201x eMath Instruction, LLC, used by permission”

FEEDBACK REQUESTED. We value your feedback about our products and services. We think others will value it, too. That’s why we may do the following (and we ask that you agree):

Use your feedback to make improvements to our products and services and even launch new products and services, with the understanding that you will not be paid or own any part of the new or improved products and services (unless we otherwise agree in writing ahead of time).
Share your feedback, including testimonials, on our website or other advertising and promotional materials, with the understanding that you will not be paid or own any part of the advertising or promotional materials (unless we otherwise agree in writing ahead of time).

SATISFACTION GUARANTEED. If you are not 100% satisfied, we will refund you the purchase price you paid within 30 days. To get a refund:

Within 30 days of your purchase,
Delete the software and all membership content from all your computers, destroy all photocopies or printouts of our materials and return all tangible copies (disks, workbooks, etc) and other materials you have received from us to:

eMath Instruction Returns Department
10 Fruit Bud Lane
Red Hook, NY 12571

TECHNICAL SUPPORT: If you are having trouble logging in or accessing your materials, or if your downloaded materials won’t open or are illegible, please notify us immediately by email at
so we can get it fixed.

NO WARRANTY. We believe in the quality and value of our products and services, and we work hard to make sure they work well and are free of bugs. But that said, we are providing our products and services to you “as is,” which means we are not responsible if something bad happens to you or your computer system as a result of using our products and services. For our full Disclaimer of Warranties, please see our Legalese version of these Terms & Conditions Here.

DISPUTES. If we have a dispute that we cannot resolve on our own, we will use Binding Arbitration instead of filing a lawsuit in a regular court (except that you can use small claims court). Binding Arbitration means our case will be decided by one or more arbitrators who are chosen and paid by all parties to the dispute. Arbitration is a faster and less formal way of resolving disputes and therefore tends to cost less.

To begin an arbitration proceeding, please send a letter requesting arbitration and describing your claim to:

eMath Instruction, Inc.
10 Fruit Bud Lane
Red Hook, NY 12571

LIMITATION OF LIABILITY. If you do win a case against us, the most you can recover from us is the amount you have paid us.

To see the Legalese version of our Terms & Conditions, please click HERE. We’ve given you the highlights above, in plain English, but it’s a good idea to look at the Legalese, too, because by checking the box below and proceeding with your purchase you are agreeing to both the English and Legalese.