Presented by: Dana TeCroney
Classification of y = (x – d)2 – 2
The purpose of this assignment is to discuss the function y = (x – d)2 – 2 as d varies. Specifically, for different values of d, we wish to discover if the shape of the graph is altered, and if the position changes.
Consider the following graph:
To see an animation of this graph as d varies from -5 to 5 and back again, press me.
If you would like to control the value of d, press me.
As you can see from the graph above, the shape of the graph is unaffected by the different values of d, however the position does change. When d = 0, y = (x – 0)2 – 2 is a parabola that opens up with the vertex at (0,-2). As d decreases, the parabola shifts to the left. As d increases, the parabola shifts to the right, with the vertex in all cases at (d,-2). This follows directly from the vertex form of a parabola y = (x – h)2 + k where (h,k) is the vertex.