Quadratic Inequalities
Completion requirements
Quadratic Inequalities
Similar to linear inequalities, it is also possible to solve quadratic inequalities in one variable by determining the values of the variable that satisfy the inequality. However, the process is usually more involved than simply rearranging an inequality to isolate the variable. Three different methods for solving quadratic inequalities will be studied. Notice that there is some overlap between the strategies and that they can all be used to answer the question “What values make this quadratic inequality true?”
If one side of a quadratic inequality is zero, the graph of the corresponding quadratic function can be used to solve the inequality. This can be done because the horizontal axis splits the graph of the function into values that are greater than zero and values that are less than zero, as shown in Figure 1. In Figure 2, the solution set to \(f(x) \gt 0\) is the blue \(x\)-values and the solution set to \(f(x) \lt 0\) is the red \(x\)-values. Notice that the solution regions are separated by the zeros of the function, which are the \(x\)-intercepts of the graph.
