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.
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):
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:
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.