**In exploring quadratic functions,
I wanted to graph**

**y = ( x -d)^2 - 2**

**and see want happens to the graph
as d varies.**

**First I looked at the graph of
y = x^2 -2, where d = 0.**

**As you see, the graph is a parabola
with the vertex at (0, -2).**

**Let's look at the general case
of the vertex form of a quadratic equation.**

**(d, k) is the vertex of the parabola.
For our purposes a = 1 and k = - 2.**

**So as d varies, the parabola
shifts along the x-axis.**

**So let's look at several graphs
of y= (x-d)^2 -2 on the same axes using different values for d,
paying close attention to the vertices of each.**

**It seems that the rule holds
that (d, -2) is always the vrtex. The shape does not change, only
the position on the x-axis.**