Building Quadratic Functions to Describe Situations (Part 1)

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

8, 9, 10, 11, 12

Overview

This is the first of several video 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 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).

Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.24
Distinguish between situations that can be modeled with linear functions and those that can be modeled with exponential functions.

Vocabulary

Linear functions
Exponential functions
Constant rate of change
Constant percent rate of change
Intervals
Percentage of growth
Percentage of decay

Knowledge

Students know:

Key components of linear and exponential functions.
Properties of operations and equality

Skills

Students are able to:

Accurately determine relationships of data from a contextual situation to determine if the situation is one in which one quantity changes at a constant rate per unit interval relative to another (linear).
Accurately determine relationships of data from a contextual situation to determine if the situation is one in which one quantity grows or decays by a constant percent rate per unit interval relative to another (exponential).

Understanding

Students understand that:

Linear functions have a constant value added per unit interval, and exponential functions have a constant value multiplied per unit interval.
Distinguishing key features of and categorizing functions facilitates mathematical modeling and aids in problem resolution.

Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.25
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Vocabulary

Arithmetic and geometric sequences
Arithmetic sequence
Geometric sequence
Exponential function

Knowledge

Students know:

That linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Properties of arithmetic and geometric sequences.

Skills

Students are able to:

Accurately recognize relationships within data and use that relationship to create a linear or exponential function to model the data of a contextual situation.

Understanding

Students understand that:

Linear and exponential functions may be used to model data that is presented as a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Linear functions have a constant value added per unit interval, and exponential functions have a constant value multiplied per unit interval.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

CUSTOM

https://aptv.pbslearningmedia.org/resource/im20-math-ep5-65/building-quadratic-…

Custom License Type (URL)

https://creativecommons.org/licenses

Comments or Notes

This resource has student task statements and practice problem worksheets.

Approved Date

2022-09-13

Design by Adaptive Theme