Factored Form of a Quadratic Function

Author: Chicago Teachers Union Quest Center

  • Description
  • Files

What we like about this lesson


  • Addresses standards F-IF.B.4 and F-IF.C.7
  • Promotes coherence by highlighting prior knowledge and pointing to the mathematics that will be built from these ideas
  • Develops students' understanding of zeros and other key features from the factored form of a quadratic function (F-IF.B.4)
  • Requires students to analyze and see the connection between quadratic functions represented graphically and algebraically
  • Requires students' use of precise course-appropriate mathematical language (MP.6)

In the classroom:

  • Offers an engaging activity that connects students' procedural skill and conceptual understanding of the key features of a quadratic function
  • Allows for whole group, partner, and individual work in one lesson
  • Provides entry points for student discussion through suggested dialogue for teachers
  • Encourages students to share their developing thinking
  • Uses explanations and representations to make the mathematics of the lesson explicit

  • Making the Shifts

    How does this lesson exemplify the instructional Shifts required by CCSSM?

    Focus Belongs to the Widely Applicable Prerequisites for College and Careers
    Coherence Builds on many key understandings from grade 8, expanding from linear to quadratic functions, and specifically calls out how this lesson falls within the progression of learning

    Conceptual Understanding: primary in this lesson (F-IF.B.4)

    Procedural Skill and Fluency: primary in this lesson (F-IF.C.7)

    Application: not addressed in this lesson

  • Additional Thoughts

    It's important to note that this sample lesson is intended to span multiple class periods, and is the second lesson in an eight-lesson unit on "Quadratics for Career and College Readiness." All other lessons in this unit can be viewed here. It is not intended for the students to meet the full expectations of the course-level standards addressed through only this lesson. For example, F-IF.B.4 requires that students also be able to interpret key features of functions in terms of their context, but this lesson addresses only the key features of the functions without context. This is something that should be addressed in later lessons. 

    The stations activity at the end of the lesson provides a powerful way to understand function behavior. It allows students to look at functions with the same algebraic format to understand how the changing values affect the graph, and to look at a group of graphed functions with the same zeros to see how their algebraic representations are different.  

    For more insight on the course-level concepts addressed in this lesson, read pages 7–9 of the progression document, Grade 8, High School, Functions.

Supplemental Resources