Lesson 8

Equations and Graphs

Lesson Narrative

In this lesson, students write an equation for a parabola and rewrite it in vertex form. Then, they match graphs of parabolas to equations. Students reason abstractly and quantitatively (MP2) as they create a parabola equation by applying the concept of distance calculations.

Learning Goals

Teacher Facing

  • Generalize (using words and other representations) the process of repeated distance calculations to derive an equation for a parabola in the coordinate plane.

Student Facing

  • Let’s write an equation for a parabola.

Required Preparation

The graphing technology is for use in the extension problem of the activity Card Sort: Parabolas.

Learning Targets

Student Facing

  • I can derive an equation for a parabola in the coordinate plane given a focus and a directrix.

CCSS Standards

Glossary Entries

  • directrix

    The line that, together with a point called the focus, defines a parabola, which is the set of points equidistant from the focus and directrix.

  • focus

    The point that, together with a line called the directrix, defines a parabola, which is the set of points equidistant from the focus and directrix.

  • parabola

    A parabola is the set of points that are equidistant from a given point, called the focus, and a given line, called the directrix.