Lesson 8
1. Lesson 8
1.7. Explore 3
Module 4: Quadratic Equations and Inequalities
Roots and Test Points Method
The next part of the lesson will focus on algebraic methods of solving quadratic inequalities. The first of these methods is based on determining the roots of the equation corresponding to the quadratic inequality. These roots are known as critical values and are used to divide the domain of real numbers into intervals.
Try This 2
Launch the Solving Inequalities 1 interactive lesson. Select Solving Inequalities 1, and then select the tutorial icon at the top of the window. Choose Solving Quadratic Inequalities in One Variable.
As you work through the interactive lesson, respond to the following questions.
- How are the critical values along the number line related to the quadratic inequality?
- How are test points selected?
- Why is only one test point selected for each interval?
Save your responses to your course folder.
Turn to “Example 3” on page 482 of the textbook to see how you can use the roots and test points approach to solve a quadratic inequality that cannot be factored. As you work through the example, look for the answers to the following questions:
- Why should you rewrite the inequality so that one side is equal to 0?
- What can be done with quadratic expressions that are not factorable?
- What strategies can you use to make exact values easier to work with?
You may want to refer to these answers when you tackle your lesson assignment.
Self-Check 2
Turn to page 485 in the textbook to practise using the roots and test points method for solving quadratic inequalities. Complete question 4. Answer