Lesson 8

Are You Ready?

 

Inequalities may often be satisfied by more than one set of values for the unknowns. For example, think of two numbers the product of which is positive. Did you think of two positive numbers, or did you choose two negative numbers? Sorting through the various possibilities is an important skill in solving quadratic inequalities. The following questions will give you a taste of what’s to come!

 

Complete these questions. If you experience difficulty and need help, visit Refresher or contact your teacher.

1. If ab > 0, which of the following statements could be true?
   
   
   1. a > 0, b > 0
   2. a > 0, b < 0
   3. a < 0, b > 0
   4. a < 0, b < 0
   
   Answer
   
   
2. If ab ≤ 0, which of the following statements could be true?
   
   
   1. a ≥ 0, b ≥ 0
   2. a ≥0, b ≤ 0
   3. a ≤ 0, b ≥ 0
   4. a ≤ 0, b ≤ 0
   
   Answer
   
   
3. Graph each of the inequalities on a number line.
   
   
   1. x > 2 Answer
      
      
   2. x ≤ 20 Answer
      
      
   3. −2 ≤ x ≤ 1 Answer
      
      
4. Solve each quadratic equation by factoring.
   
   
   1. x2 + 3x − 18 = 0 Answer
      
      
   2. 3x2 − 10x + 8 = 0 Answer
      
      
5. Solve each quadratic equation by using the quadratic formula.
   
   
   1. x2 − 4x − 1 = 0 Answer
      
      
   2. 3x2 + 11x + 10 = 0 Answer

How did the questions go? If you feel comfortable with the concepts covered in the questions, move on to Discover. If you experienced difficulties, use the resources in Refresher to review these important concepts before continuing through the lesson.