The students were instructed to go to this link and match up as many parabolas as they could using the sliders a,b,c, and d. After playing around with this graph, and another set of exponentials, and talking it over with their groups, we formalized what each of the letters did.
We looked at the equation: y=a*f(b(x-c))+d and wondered why d worked opposite of c. Why did the c need a negative where the d didn’t? If you rewrite it as y-d=a*f(b(x-c)) then it’s more clear what is happening. Likewise for the a and the b. Why did they act opposite of each other? Rewrite it as (1/a)*(y-d) = f(b(x-c)) and then it’s more obvious why they are acting in different directions. Who is to blame about the y= form for everything? Can I blame Texas Instruments?