Module 3: Lesson 3

 

Self-Check 3

1. Questions 3.a., 3.b., and 5 on page 148 of the textbook
   3.  
      1. In the graph the three roots can be identified by inspection.
         
         
          
         x = −3            x = −2            x = 1
         
         Each of these roots can be used to generate an equation.
         
         
          
         
         
         While this is sufficient for an answer, the equation could also be expanded to obtain the following:
         
         
          
         
         
      2. In the graph the three roots can be identified by inspection.
         
         
          
         x = −4            x = 1            x = 3
         
         These roots can be used to generate an equation. Note the end behaviours of the graph. Since the graph starts in quadrant 2 and ends in quadrant 4, the a-value of the polynomial function must be negative.
         
         
          
         
         
         Expanding the answer would give the following:
         
         
          
         
         
   5. The reasons for the justification may vary. A sample answer to each is provided.

      1. B. The graph is a cubic polynomial with a positive leading coefficient, which means that the graph will start in quadrant 3 and end in quadrant 1.

      2. D. The graph is a cubic polynomial with a negative leading coefficient, which means that the graph will start in quadrant 2 and end in quadrant 4.
         
      3. C. The graph is a quartic polynomial with a y-intercept of 3.
      4. A. The graph is a quartic polynomial that does not have a y-intercept of 3.
         
   
   
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