Lesson 18

Applying the Quadratic Formula (Part 2)

Lesson Narrative

In earlier lessons, students saw that the quadratic formula can be used to solve any quadratic equation, but also that it might not be the most practical approach for all equations. Here, students deepen their understanding about the merits and potential drawbacks of using the quadratic formula. They pay close attention to each step in the solving process and analyze errors commonly made when applying the formula. Students also consider how to verify that the solutions they obtained with the quadratic formula are correct.

In analyzing the solution process and checking their work and the work of others, students practice attending to precision and critiquing the reasoning of others (MP6, MP3).

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. Consider making technology available.

Learning Goals

Teacher Facing

  • Analyze and critique (orally and in writing) solutions to quadratic equations that are found using the quadratic formula.
  • Determine whether a given value is a solution to a quadratic equation.

Student Facing

  • Let’s use the quadratic formula and solve quadratic equations with care.

Required Materials

Required Preparation

Be prepared to display a graph for all to see in the activity synthesis of “Sure About That?” There is an image to display if graphing technology is not available.

Learning Targets

Student Facing

  • I can identify common errors when using the quadratic formula.
  • I know some ways to tell if a number is a solution to a quadratic equation.

CCSS Standards

Building On

Addressing

Building Towards

Glossary Entries

  • quadratic formula

    The formula \(x = {\text-b \pm \sqrt{b^2-4ac} \over 2a}\) that gives the solutions of the quadratic equation \(ax^2 + bx + c = 0\), where \(a\) is not 0.