Horizontal
Shifts |

One can observe from the above investigations that when a quadratic function is in the form , positive values of d cause a horizontal shift of the parabola to the right, the number of

units d. When d is a negative value, the graph will shift horizontally to the left d units.

Vertical
Shifts |

Given the form of a parabola as , the vertex is (d, k). Let's look at positive and negative values for k. For this exploration h will be zero.

Looking at the exploration given, positive values of k cause a vertical shift up k units. Negative values of k

cause a vertical shift down k units. Therefore, from this we see that the vertex is (d, k) when given the form .

Changing the value of d causes a horizontal shift and changing the value of k causes a vertical shift. Changing these values will not cause any change in the shape of the parabola.