Lesson 17

Applying the Quadratic Formula (Part 1)

Lesson Narrative

In this lesson, students return to some quadratic functions they have seen. They write quadratic equations to represent relationships and use the quadratic formula to solve problems that they did not previously have the tools to solve (other than by graphing). In some cases, the quadratic formula is the only practical way to find the solutions. In others, students can decide to use other methods that might be more straightforward (MP5).

The work in this lesson—writing equations, solving them, and interpreting the solutions in context—encourages students to reason quantitatively and abstractly (MP2).

Learning Goals

Teacher Facing

  • Interpret (orally and in writing) the solutions to quadratic equations in context.
  • Practice using the quadratic formula to solve quadratic equations, rearranging the equations into $ax^2+bx+c=0$ if not already given in this form.

Student Facing

  • Let’s use the quadratic formula to solve some problems.

Required Materials

Learning Targets

Student Facing

  • I can use the quadratic formula to solve an equation and interpret the solutions in terms of a situation.

CCSS Standards

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.