Second Degree Inequalities

In this section, we apply our knowledge of non-linear equations to the study of non-linear inequalities/second-degree inequalities. When solving linear inequalities in two variables, we learned a boundary line separated the solution region from the non-solution region. We carry this concept over when graphing a non-linear inequality. First, we replace our inequality symbol with an equality symbol. We then graph the resulting equation as our boundary. Once this is done, we can use a test point to determine where the solution region lies. Recall that if a point that is not on our boundary works as a solution, we shade the region that contains that point. If the point does not work as a solution, we shade the region opposite of the point. We will also examine how to solve a system of non-linear inequalities. For these problems, we begin by graphing each inequality. We can then graph our solution to the system as the overlap between the graphs.