This is the first of several lessons in which students construct quadratic functions to represent various situations. Here they investigate the movement of free-falling objects. Students analyze the vertical distances that falling objects travel over time and see that they can be described by quadratic functions. They use tables, graphs, and equations to represent and make sense of the functions. In subsequent lessons, students build on the functions developed here to represent projectile motions, providing a context to develop an of the zeros, vertex, and domain of quadratic functions.

To express the relationship between distance and time, students need to see regularity in numerical values and express that regularity (MP8).