Years ago, the Friday Fave attended a conference session by Zalman Usiskin who
claimed there that all parabolas are similar to each other.
The Fave is convinced of the truth of this claim in a formal way, but still thinks it sounds preposterous and obviously false. If you squish a square in one direction it is no longer a square. If you squish a rectangle in one direction, you still have a rectangle but it is no longer similar to the original. So clearly a parabola described by f(0.5x) cannot be similar to the one that f(x) describes.
It is in the spirit of such claims about the relationships among graphs of functions under transformations that the Friday Fave offers up a new What’s My Transformation? in which students transform parangulas using function notation.
What is a parangula? you ask!
Well, my friends, a parangula—like a line or a parabola—is a geometric object described algebraically, which you may transform by translating, stretching, squishing, and reflecting in order to learn some general algebraic tools for working with these in the future.
What is more, this parangulas activity is featured in one of TWO new activity bundles over at teacher.desmos.com. The Fave is pleased to share with all of you a new Conics Bundle, and a new Function Transformations bundle.
So head on over and get your students started with parangulas. After all, there is just one parangula in the world, and just one line, and just one parabola. Usisikin was right about that.