Quadratics In the X-B Plane
By: Lacy Gainey



We can see that the graph is a hyperbola with two asymptotes.  One of these asymptotes is located at x=0, but the other one is a little harder to locate.

From the graph, we can see that the other asymptote is located at x = -y.

Is this what you expected?


Our graphs still contain a hyperbola and two asymptotes.  As c increases, the hyperbola seems to moving farther away from the orgin.

We can see that the line y=5 intersects the curve twice. We have two negative roots when y > 2 and one negative root when y=2.

The line y= -5 also intersects the curve twice.  This time we have two positive roots when y< -2 and one positive root when y= -2.  Additionally, there are no real roots when -2 < b < 2.

We can see that when c = -1, there will always be two real roots for [5].

Click here to return to Lacy's homepage