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).