In this lesson, students graph functions to find the zeros and then write associated equations that would be solved with the values they find. In the associated Algebra 1 lesson, students do a similar process to determine whether a quadratic expression can be easily factored. Students reason abstractly and quantitatively (MP2) when they use equations to represent the zeros on a graph.

The purpose of the discussion is to show the relationship between zeros of a function and solutions to associated equations. Here are some questions for discussion:

• “A function has zeros at 2 and 3. Write a quadratic equation with solutions at those same values.” (The equation has solutions at 2 and 3.)
• “A function has zeros at and -2. Write a quadratic equation with solutions at those same values.” (The equation or the equation each have solutions at and -2.)

The purpose of this activity is to give students a chance to work with a partner to connect quadratic expressions in different forms. In this partner activity, students take turns matching expressions in factored form with associated functions in standard form. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

Once all groups have completed the matching, discuss the following:

• “Which matches were tricky? Explain why.” (The two expressions that had as a term were difficult because I had to look more closely at all of the terms and not just a few of them.)
• “Did you need to make adjustments in your matches? What might have caused an error? What adjustments were made?”