Lesson 6

Try This 3

1. Consider the following quadratic-quadratic system.
   
   
    
   y = 3x2 + x − 2
   
    
   y = x2 + 2x + 1
   
   Solve this system algebraically by following this example shown for the linear-quadratic system:
   
   
    
   
   
   
   1. Reduce the system to a single equation in one variable using elimination.
      
      
   2. Determine the solution(s) algebraically to the resulting equation using an appropriate strategy.
      
      
   3. Verify your solution(s) algebraically.

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Share 3

1. Compare your solution strategies with a partner. Discuss the relative advantages and drawbacks of the strategies for
   
   
   1. reducing the system to a single equation
      
      
   2. solving the quadratic equation
      
      
2. Why is it difficult to solve this system by eliminating the x-variable instead of the y-variable?
   
   
3.  
   1. With your partner, manipulate the system so that you can eliminate the x2-term. Graph the resulting equation, as well as the equations in the system.
      
      
       
      y = 3x2 + x − 2
      
       
      y = x2 + 2x + 1
      
      
   2. What do you notice about graphing the equations from part a?
      
      
4. How can a strategy for solving the original system be developed based on your observations from question 3?

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Self-Check 2