In this activity students rewrite quadratic equations into the form , then identify the values for and , then use those values to find . In the associated Algebra 1 lesson, students work with the quadratic formula. Identifying the values to be used in the quadratic formula and using the values to find the discriminant supports students to use the quadratic formula in its entirety. This practice familiarizes students with the structure of standard form quadratic equations and the quadratic formula (MP7).

The purpose of the discussion is to recognize any preliminary work that needs to be done before using the quadratic formula. Select students to share their solutions. Here are some questions for discussion:

• “For the first question, Noah says that , and . His paper is given full credit. Explain why those values are correct.” (Subtracting or adding each term to both sides results in the equation , which means Noah’s values are correct.)
• “Before selecting and , what needs to be done to the equation to find the values accurately?” (The equation needs to be rewritten so that one side of the equation is zero and the other side is in standard form.)
• “When you find , what are the first things you need to do for order of operations?” (Squaring the value for and multiplying 4, , and should be done before subtracting.)

In this activity, students are not told a specific method to use to solve quadratic equations. In the associated Algebra 1 lesson, students are introduced to the quadratic formula to solve quadratic equations. Here, students are reminded of the other methods, which can be more or less efficient for solving equations. When students are clear in their reasoning for the method they choose, they attend to precision (MP6).

Monitor for students who use these different strategies:

• Factoring
• Completing the square

The goal of the discussion is to evaluate the methods students already know for solving quadratic equations.

Display 2–3 approaches from previously selected students for all to see. Use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:

• “Did anyone solve the problem the same way but would explain it differently?”
• “How are factoring and completing the square the same? How are they different?”
• “Are there any benefits or drawbacks to one representation compared to another?”