Last school year, I remember my students had a miserable time remembering the different ways that a function was transformed when they looked at the equation. (Does minus 4 here mean that the graph goes up, down, left, or right? Does a negative in front mean the parabola opens up or down? Why would I want standard form versus vertex form?) This year, I decided we needed some memory tricks for these along with our notes and our families of functions scrapbook.
Cute trick #1 is an oldie but a goodie. If the a value is negative, the graph is opening down, so "frowning." Negative=frown, so that's should be an easy one to remember.
Cute trick #2 is inspired by my kids last year who struggled with the idea of vertical stretch and shrink. They so wanted to talk about horizontal stretch and shrink when they viewed graphs, but that's a bit backwards since an equation in the form y = 3x^2 has an a value greater than 1 which they understood to be an increase in size. To that end, I did a little demo today in MS Word with clip art pigs. I started with three equally sized pigs. I kept the "parent" the same. I changed the other two pigs based on a values of 2 and 1/2. Tonight, I added the annotations and tomorrow this will be on my wall.