**Graphs in the xa plane.**

Consider the equation

Now graph this relation in the xa plne. We get the following graph.

If we take any particular value of a, say **a **= - 3, we can add a line parallel to the x-axis. In addition, a parallel line will intersect with the original graph, and the intersection points correspond to the roots of the original equation for that value of **a**. We have the following graph.

For each value of **a **we select, we get a horizontal line. It is clear on a single graph that we get no real roots of the original equation when **a > 0.25**, one negative real root when **a = 0.25** and **a = 0**, two negative real roots when** 0 < a < 0.25**, one negative and one positive roots when **a < 0**.

Consider the case when** c = - 1** rather than **+ 1**.

When I graph other values of **c** on the same axes, the graphs are expressed like these.

When c = 0, it becomes a graph of , and it is on quadrant II and IV. When c < 0, graph is on quadrant I, II, and IV. when c > 0, graph is on quadrant II, III, and IV.