# Lesson 5

Building Quadratic Functions to Describe Situations (Part 1)

### Lesson Narrative

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 understanding 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).

### Learning Goals

Teacher Facing

• Explain (orally and in writing) the meaning of each term in a quadratic expression that represents the height of a free-falling object.
• Use tables, graphs, and equations to represent the height of a free-falling object.
• Write quadratic functions to represent the height of an object falling due to gravity.

### Student Facing

• Let’s measure falling objects.

### Required Preparation

Be prepared to display a GeoGebra applet for all to see during the synthesis of the activity "Galileo and Gravity."

### Student Facing

• I can explain the meaning of the terms in a quadratic expression that represents the height of a falling object.
• I can use tables, graphs and equations to represent the height of a falling object.