# 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.

### Student Facing

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

### 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.