Lesson 8

Lesson 8: Solving Quadratic Inequalities in One Variable

Focus

If you had unlimited resources to design a community that minimized its impact on the environment, what would your design look like? What kind of materials would be used to construct the buildings in your community? How would you reduce carbon emissions from transportation?

Building communities that fit into the environment isn’t a new idea. The Anisazi of the southwestern United States built communities using local materials. Similar communities can be found in Mali and in the city of Petra, in Jordan. These buildings used ideas that environmental designers are still using today. Building into a cliff provides thermal stability—have you seen homes that seem to be built underground except for one wall? Have you ever opened a window after a hot summer day to get the cooler evening air into a room? Search for “environmental city design” to find some striking images and interesting ideas.

In this lesson you will study quadratic inequalities in one variable. You will learn how to solve these inequalities by graphing and by algebraic methods. You will also model and solve problems with quadratic inequalities, including one that deals with a special type of eco-friendly construction material.

Outcomes

At the end of this lesson you will be able to

• determine the solution of a quadratic inequality in one variable using a variety of strategies
  
  
• represent and solve a problem that involves a quadratic inequality in one variable
  
  
• interpret the solution to a problem that involves a quadratic inequality in one variable

Lesson Questions

You will investigate the following questions:

• What principle is common to all strategies for solving quadratic inequalities?
  
  
• How can you tell when a problem can be modelled by a quadratic inequality in one variable?

Assessment

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

• completion of the Lesson 8 Assignment (Download the Lesson 8 Assignment and save it in your course folder now.)
  
  
• course folder submissions from Try This and Share activities
  
  
• additions to Module 4 Glossary Terms and Formula Sheet
  
  
• work under Project Connection