Lesson 12

Forms of Quadratic Equations

These materials, when encountered before Algebra 1, Unit 7, Lesson 12 support success in that lesson.

Lesson Narrative

In this lesson, students practice working with quadratic expressions written in factored form as perfect squares and notice patterns in the equivalent standard form. In the associated Algebra 1 lesson, students begin the process of completing the square. Being fluent with recognizing perfect squares in standard form and patterns in the coefficients help students recognize what is needed to complete the square. Students express regularity in repeated reasoning (MP8) when they notice patterns in the type of coefficients that match the given squares.

Learning Goals

Teacher Facing

  • Identify patterns of quadratic expressions as a result of rewriting $(x+n)^2$ in standard form.
  • Recognize equivalent expressions in the form $(x+n)^2$ and in standard form.

Student Facing

  • Let’s explore different forms of quadratic equations.

CCSS Standards

Building Towards