While we've studied quadratics a lot, we never seem to do enough applications. In this blog, you will search the internet for applications. Find at least one. If you discuss one, discuss in detail and well. If you discuss two, then you can write less about each. Here are some hints:
So your job is to not just say, hey, it's a projectile path.... or hey, a parabola is the shape of those whispering things... your job is to explain why this is a parabola. Find something about the FOCUS, or the LATUS RECTUM or the DIRECTRIX. Explain something NEW about the parabola. Below is a hint. Ask Purple Math or Khan Academy to help you out with this. I found HOT MATH to be the simplest explanation.
Beware of catenary arches posing as parabolic arches. When you google "parabola" you'll find images of catenary arches. Be sure you are familiar with what those arches are before you write about them in your blog. OR..... Write a blog about catenary arches. What are they? How are they formed? They are kind of cool.
Also beware of semicurcular Roman Arches. These are not parabolic either. In short, be careful about your choices. While you can use a parabolic model to fit catenary and semicircular shapes, this blog asks you to be more accurate mathematically and theoretically. There's some bad information out there on line!
Someone who understands the difference between catenary arches in architecture and parabolic arches in architecture is Ivars Peterson in his blog, The Math Tourist.
