In this lesson, students learn that a parabola is the set of points equidistant from a given point, or focus, and a given line, or directrix. Students explore the relationship between the positioning of these elements and the resulting shape of the parabola. Then they practice using distance calculations to test if particular points lie on given parabolas. This work helps prepare students to write an equation for a parabola, in an upcoming lesson.

Students have the opportunity to attend to precision in language (MP6) as they articulate what they notice and wonder about a diagram showing several points equidistant from a given point and line. They continue this process throughout each activity as they more carefully describe the relationship between the points on a parabola, the focus, and the directrix. 

One of the activities in this lesson works best when each student has access to a device that can run the Desmos applet, because students will benefit from seeing the relationship in a dynamic way.