Consider graphs in the xa
Consider the equation
, where a is from -10 to 10.
These are the graphs when a = -9, -6, -3, 0, 3, 6, 9.
If you want to see the animation, please click here .
In this animation, as the value of a changes, the graph is moving.
We can tell the roots of the equation by looking at the points of the x-intercept of the graph.
Now graph this in the xa plane. We get the following animaition.
After sloving the equation for a, I draw the curve in purple.
Instead of moving the original grph, let the red line move by the value of a.
The number of the point of interscetion between the purple curve and the red line tell us the number of root of the original equation.
Also the x-coordinates of the point of intersection give the root of the original equation.
Click here to see the animation.
In the following graphs, c = 10 and -10.