1. Lesson 7

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

 

Lesson 7: Graphing Linear and Quadratic Inequalities

 
Focus

 

This is a photo of several levels of a shopping mall.

© Heng kong Chen/492933/Fotolia

A popular concept amongst urban planners is the development of “cities within cities.” These developments are designed to be one-stop shopping destinations as well as recreation and entertainment centres. More than your typical shopping mall, these complexes include restaurants, hotels, business offices, and even residential space.

 

The city-within-a-city concept has been particularly popular in Asian countries. In some Asian countries, booming economies and increasing consumer and housing demand have driven architects and designers to create all-encompassing mega-complexes.

Mathematics can help architects design complexes that meet the needs of residents and consumers alike.

 

In this lesson you will learn how you can use linear and quadratic inequalities to represent multiple variables, much like an architect might use mathematics to guide the development of a project involving multiple factors.

 

Outcomes

 

At the end of this lesson you will be able to

  • explain, using examples, how test points can be used to determine the solution region that satisfies an inequality

  • explain, using examples, when a solid or broken line should be used in the solution for an inequality

  • sketch, with or without technology, the graph of a linear or quadratic inequality

  • solve a problem that involves a linear or quadratic inequality

Lesson Questions

 

You will investigate the following questions:

  • How are the properties of linear and quadratic inequalities in two variables related to their graphs?

  • How are linear and quadratic inequalities in two variables applied in design?

Assessment


Your assessment may be based on a combination of the following tasks:

  • completion of the Lesson 7 Assignment (Download the Lesson 7 Assignment and save it in your course folder now.)

  • course folder submissions from Math Lab, Try This, and Share activities

  • additions to Module 4 Glossary Terms and Formula Sheet

  • work under Project Connection

Materials

 

You will need a ruler and graph paper.