In this lesson, students connect the equation of a parabola with the features of its graph. First, they find the distance between a point on the parabola and the focus by using the vertical distance to the directrix. Then students match graphs of parabolas to the equations, as they use more precise language to describe the features of the graph and the structure of an equation (MP6). Then students apply repeated reasoning from throughout the lesson to generalize a process for writing an equation of a parabola (MP8).

In this and subsequent lessons, students will encounter parabolas whose directrix is horizontal, so the process for writing equations is not for a general parabola, but for a specific class of parabolas that correspond to parabolic functions.