How do we solve quadratic inequalities graphically?

              In Algebra I we learned how to solve linear inequalities both algebraically and graphically. Now in Algebra II we take this concept and apply it to solving quadratic inequalities. Let's solve the quadratic inequalities –x² + 4 < 0. First we factor so that we can find where the parabola crosses the x axis and that looks like this: 

–x² + 4 = 0 

x² – 4 = 0 

(x + 2)(x – 2) = 0 

x = –2  or  x = 2 

            Now that we know the roots are -2 and 2 we can plot those points. Because its a negative inequality we know the parabola opens down. We can plug in numbers to the equation to find other points to plot and in the end we'll have this: 

                      To solve the inequality we need to find out which points where the graph is below the axis or in other words where the y - values are less than zero. To find where we need to shade we can pick a test point inside or outside of the parabola and the one that's true indicates where we need to shade. In this case we shade outside of the parabola leaving your graph to look something like this: 

               And our final written solution is x < –2 or x > 2.