Comparing Quadratic and Exponential Functions

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

8, 9, 10, 11, 12

Overview

In this video lesson, students investigate how quantities that grow quadratically compare to those that grow exponentially. They discover the reason that increasing exponential functions also eventually surpass increasing quadratic functions. By examining successive quotients for each type of function, students see that the outputs of quadratic functions are not multiplied by the same factor each time the input increases by one. In fact, these successive quotients get smaller as the inputs increase, while the outputs of the exponential function have the same multiplier. As they compare the two types of functions, they develop their understanding of quadratic expressions and how the shape of the graph differs between the two types of functions.

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.A1.26
Use graphs and tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

Vocabulary

Increasing exponentially
Increasing linearly
Polynomial functions

Knowledge

Students know:

Techniques to graph and create tables for exponential and polynomial functions.

Skills

Students are able to:

Accurately create graphs and tables for exponential and polynomial functions.
Use the graphs and tables to present a convincing argument that the exponential function eventually exceeds the polynomial function.

Understanding

Students understand that:

Exponential functions grow at a faster rate than polynomial functions after some point in their domain.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

PD

https://aptv.pbslearningmedia.org/resource/im20-math-ep4-64/comparing-quadratic…

Comments or Notes

This resource contains student practice problems and student task statements.

Approved Date

2022-09-13

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