I asked what they noticed when I wrote:
While we were having this discussion I had a huge coughing fit and had to leave the room as I could neither talk nor breathe very well! A little water and a cough drop helped me continue, but I'm not really sure what I said beyond pointing out the similarities of these two equations. After the coughing fit I did take it one step further and showed them that the equation of any function can be written in this form - in other words, it's not going away. However, I also told them that if they would like to continue using y = mx + b to find the equation of a line, they are more than welcome to do so.
On to the meat of today's lesson:
We worked through an example of each, with emphasis on making a plan before diving in. I also had them draw each one and we checked the reasonableness of our answers at each step against the diagram.
Here is today's handout. I did not give homework as I want them to spend time working on their parabolic art.