In this activity, students are asked about ways to check solutions for equations and apply the zero product property to solve a quadratic equation in a new context. Students construct viable arguments and critique the reasoning of others (MP3) when checking another person’s work. In the associated Algebra 1 lesson, students examine ways to check their work when using the quadratic formula. This activity supports students to use additional methods to check their solutions when solving equations. Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).

The purpose of the discussion is to give students methods for checking their work. Select students to share their solutions and methods. For the second question, ask students what methods they used to solve the quadratic equation. Here are some questions for discussion:

• “What does the zero product property say and why does it hold for the equation in Priya's brother’s work?” (The zero product property says that when two things are multiplied to get 0, at least one of the things must be 0. From Priya's brother’s work, he has that two things multiply to make 0: and , so one of those must be equal to 0.)
• “How can you check that your solutions, -2 and 4, work for the original equation?” (Substitute the values into the original equation or look at a graph.)

In this activity, students list some of the steps in the process of using the quadratic formula to solve a quadratic equation. They make sense of problems and persevere in solving them (MP1) by analyzing each step of the solution. In the associated Algebra 1 lesson, students examine some common errors when using the quadratic formula. This work supports students to be reminded of the order of operations as well as determining which values to use in the quadratic formula.

The purpose of the discussion is to remind students of the order in which things should be done when using the quadratic formula.

Direct students’ attention to the reference created using Collect and Display. Ask students to share their solutions. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.

1. Make sure the equation is in the form .
2. Find from the equation.
3. Substitute the values into the quadratic formula (it may help to put each value in parentheses).
4. Evaluate all terms in the quadratic formula: .
5. Subtract the values inside the square root.
6. Find the square root of the value.
7. Write as 2 separate solutions, one using addition and one subtraction based on the .
8. Add and subtract in the numerator for each solution.
9. Divide the numerator by the denominator.
10. Check your work (substitute the values into the original equation or graph).