Let's
look at 
for different values of d.
This graphs a parabola with vertex at (0,-2) that opens up. So notice that the center is at (d,-2)
***Notice a shift to the right when we subtract from d. Also notice that the centers remain at (d,-2)
RED:
Center (1,-2)
BLUE:
Center (2,-2)
GREEN:
Center (3,-2)
***Notice a shift to the left when subtracting a negative number from d. (Adding to d). Centers still remain at (d,-2).
LIGHT
BLUE:
Center
(-1,-2)
YELLOW:
Center
(-2,-2)
GRAY:
Center (-3,-2)
From this demonstration we can see that when d increases, the graph moves to the right and when d decreases, the graph moves to the left. However, the size of the graph remains the same when moving in increments of one.
What if d is less than 1? Let's try d = .5.
PURPLE:
Center (0.5,-2)
BLACK:
Center (0,-2)
Notice that this did not change the size, it just changed the distance of the shift. Also the center pattern still holds.
To look at the continuous motion as d changes, CLICK HERE!
FURTHER INVESTIGATION:
What if other parameters are changed?
Example: Let's change the -2.
where d = and n ranges from -5 to 5.
Click HERE to see what this does to the graph.
After looking at the demonstration, we can infer that the change in the n in this equation changes the position of the vertex of the parabola. We can also conclude that the center of the parabola will always be at (d,-n).