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 freefalling 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 freefalling object.
 Use tables, graphs, and equations to represent the height of a freefalling 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."
Learning Targets
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.
CCSS Standards
Glossary Entries

quadratic function
A function where the output is given by a quadratic expression in the input.