Explorations of Parabolas

By: Ginger Rhodes

We will
investigate the effect varying d has on the graph of .

Lets begin
by looking at the graph when

d =
0.

Notice the
vertex of the graph is at the point (0,-2).

Now, lets
take a look at the graph when

d = 1.

Notice the
vertex of the graph is at the point (1, -2).

It seems
like the value of d is the x-coordinate of the vertex. Lets look at several more cases to
check our conjecture.

By looking
at these graphs I can see that the position of the graph changes when d
changes, but the shape and size stays the same. From the graph I see that the x value of the vertex is the
value of d.