MPM2D - Day 33: A Little Algebra with Quadratics

As my students get more comfortable working with quadratics, some have figured out how to calculate the 'a' value when determining the equation given a graph. I decided that it was time for everyone to see how to do this. My plan was to work through four examples together, which you can find here. I would like to say that I thought about where these would take us, but I didn't. I love how things turned out and need to make more time in my planning to ensure that I don't miss going down a path when it presents itself.

We started by writing down the three forms of a quadratic equation on the whiteboard (I wrote, but they told me what to write), and needed to clarify that the vertex was at (h,k). Then we worked on the first example, beginning with "Which form of the equation should you choose?":

This one was next:

At this point they had a fairly solid understanding of how to find the equation and they impressed me when they worked on example 3 - many students didn't need any prompting to find the x-value of the y-intercept, which is traditionally a common issue.

I asked them the do example 4 and, if they finished quickly, to do it a different way.

And then it just seemed natural to ask them to...

I love being able to connect to work that we have already done like this. I also know from checking homework that many students have had trouble correctly expanding and simplifying from vertex form. This gave me an opportunity to see what errors they were making and they all were able to experience success with this type of question.

I then asked what they knew about the graph from the equation in standard form. I wrote down all their responses without comment and then we went to Desmos to see the graph and adjust the answers.

I really like how it all came together. I am trying to ensure that my students don't simply learn a collection of skills, but rather that they understand how they fit together. I think that several pieces of the (quadratics) puzzle clicked today.

Here is today's homework set.