Lesson 16

The Quadratic Formula

Lesson Narrative

In this lesson, students encounter the quadratic formula and learn that it can be used to solve any quadratic equation. They use the formula and verify that it produces the same solutions as those found using other methods, but can be much more practical for certain equations.

In upcoming lessons, students will continue to develop their understanding of the formula and its structure by using it to solve contextual problems and by analyzing its parts. After students have gained some experience working with the formula, they will investigate how it is derived.

Using the quadratic formula to solve equations requires students to attend carefully to the parameters in the given equations (MP6) and to apply different properties of operations flexibly as they reason symbolically (MP2).

Learning Goals

Teacher Facing

  • Recognize that the solutions obtained using the quadratic formula are the same as those found by using factored form or by completing the square.
  • Use the quadratic formula to solve quadratic equations of the form $ax^2+bx+c=0$.

Student Facing

  • Let’s learn a formula for finding solutions to quadratic equations.

Required Materials

Learning Targets

Student Facing

  • I can use the quadratic formula to solve quadratic equations.
  • I know some methods for solving quadratic equations can be more convenient than others.

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.