Investigation: Introducing Systems of Non-Linear Equations

Introducing Systems of Non-Linear Equations

1. The graphs of two non-linear systems are shown.
   
   
   
1. Describe a scenario that would lead to each graph.
   
   
2. What does the intersection of the curves represent in each scenario.
   
   
   
2. The following is a system of quadratic equations.
   
   
   • Equation 1: \(y = x^2 + 2x +3\)
     
     
   • Equation 2: \(y = -x^2 - 2x +3\)
     
     
   1. Complete the following tables of values.
      
      

      Equation 1
      \(x\)	\(y\)
      \(-3\)
      \(-2\)
      \(-1\)
      \(0\)
      \(1\)
      \(2\)
      \(3\)

      Equation 2
      \(x\)	\(y\)
      \(-3\)
      \(-2\)
      \(-1\)
      \(0\)
      \(1\)
      \(2\)
      \(3\)

      
      
   
   
   
   2. Using your tables, state the solution(s) to the system.
      
      
   3. Sketch a graph of the system of equations.
      
      
      
      
   4. Using the graph, state the solution(s) to the system.
      
      
   5. Verify your solutions by substituting them into the original equations.