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Lesson 7

1. Lesson 7

1.8. Explore 4

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

Writing an Inequality to Describe a Given Graph

 

You have learned how to graph linear and quadratic inequalities in two variables. You will now learn how to write an inequality to describe a given graph.

 

Try This 4
  1.  
    1. For the graph shown, write the equation of the boundary.

    2. What inequality sign should be used? Write the inequality.

      This shows the graph of a parabola with vertex (–2, –4) and x-intercepts at (–4, 0) and (0, 0). The region below the curve is shaded.
  2. In the graph shown, the equation of the boundary is given. Replace the equal sign in the equation 2x − 3y = 6 with an inequality symbol such that the resulting inequality describes the graph.

     
    This shows the graph of a linear inequality with dashed boundary 2x–3y = 6. The half-plane above the boundary is shaded.

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Share 2

 

With a classmate, compare your strategies for each of the exercises in Try This 4. If both you and your partner used the same strategy, see if you can develop a second strategy together. Discuss the relative benefits and drawbacks of each strategy.