The purpose of this Warm-up is to practice solving quadratic equations and determine how reasonable the solutions are in a situation. While quadratic equations often result in two solutions, sometimes only one of the values makes sense for the context. As students work with solving quadratic equations and connecting them to real situations, they should be mindful that some solutions may not be reasonable.

In this activity, students critique a statement or response that is intentionally unclear, incorrect, or incomplete and improve it by clarifying meaning, correcting errors, and adding details (MP3).

The purpose of the discussion is to share methods for solving the quadratic equation as well as determining that some solutions may not be reasonable in a situation.

Use Critique, Correct, Clarify to give students an opportunity to improve a sample written response explaining if both solutions are reasonable by correcting errors, clarifying meaning, and adding details.

• Display this first draft:
  Yes, both solutions make sense because solutions happen at the points where the output is 0. if the -values of -1 and 4 are substituted into the original function, the answer would be 0.
  Ask, “What parts of this response are unclear, incorrect, or incomplete?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.
• Give students 2–4 minutes to work with a partner to revise the first draft.
• Select 1–2 students or groups to slowly read aloud their draft. Record for all to see as each draft is shared. Then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.

In this activity, students interpret a quadratic equation in context. In the associated Algebra 1 lesson, students solve quadratic equations in context using the methods they learned throughout the unit. The work of this activity supports students to interpret the context to set up the equations so their work can focus on solving the equations. When students decide if they will graph by hand or by using technology, they are using appropriate tools strategically (MP5). Students reason abstractly and quantitatively (MP2) when interpreting values in the context of the situation.

The goal of this activity is to give students another opportunity to analyze a quadratic equation within the context of a situation. In the associated Algebra 1 lesson, students solve quadratic equations in context using the methods they learned throughout the unit. The work of this activity supports students to interpret the context to set up the equations so their work can focus on solving the equations. When students decide if they will graph by hand or by using technology, they are using appropriate tools strategically (MP5). Students reason abstractly and quantitatively (MP2) when interpreting values in the context of the situation.