The purpose of this discussion is for students to notice some common features of functions that could indicate zeros of the function. Select students to share their solutions. Here are some questions for discussion:

• “Both and have 2 of the same numbers that make the equation zero. What do you notice about them?” (They are equivalent functions. Multiplying by 0.5 results in .)
• “Notice that can be factored and written as and can be written as . Use the distributive property to check that they are the same. Compare these factored forms to the factored forms for all of the other functions. What do you notice looks the same? Do you think that has anything to do with the reason all the functions evaluate to zero?” (All of the forms have as a factor. I do think that has to do with why all the functions evaluate to zero.)

In this activity, students match equivalent quadratic equations in factored and standard form. In the associated Algebra 1 lesson, students will work with quadratic equations in factored form. The additional fluency students gain from this activity will help students when making sense of the equations they will see in Algebra 1 lessons.

Students sort different equations during this activity. A sorting task gives students opportunities to analyze representations, statements, and structures closely and make connections (MP2, MP7).

Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).

The goal of this discussion is to make connections between equations in different forms.

Once all groups have completed the Card Sort, discuss the following:

• “Which matches were tricky? Explain why.”
• “Did you need to make adjustments in your matches? What might have caused an error? What adjustments were made?”