To begin our investigation of the role that d plays in the quadratic,
, it will be necessary to let d assume different values
and then graph on the same axes to obtain a picture of what is occuring
The equations that will be graphed are as follows:
(Equations are graphed in order from right to left)
Varying d in the equation causes the graph to shift in position
When d=3, we would assume then that the graph would move three places
to the right from the original graph where d=0. This is verified by the
graph of where d=3. So the vertex
is at (3,-2).
If we want the graph to shift 8 places to the right, all we have to do
is alter d by letting d=8. So the equation becomes , where the vertex
should be at (8,-2).
It is important to note here that it appears that d is equal to a positive three in the equation . Nevertheless, the value of d is actually -3. Notice when we substitute d = -3 into the original equation . Simplifying leads to the resulting equation: .
Using this graphing technology allows students opportunities to see the effects that changing one variable, namely d, has on the graph. It is one thing to tell students that changing d translates the graph horizontally. It is however another to let students see for themselves and discover on their own that d causes horizontal shifting of the graph. When students are allowed to make generalizations and draw conclusions on thier own, they experience a sense of involvement and value their learning much more as compared to being told what d does.