The formula to calculate the number of posts is:

\[ \text{Number of Posts} = \frac{\text{Fence Length (ft)}}{8} + 1 \]

The formula to calculate the total number of rails is:

\[ \text{Total Number of Rails} = (\text{Number of Posts} - 1) \times \text{Number of Rails} \]

The formula to calculate the number of pickets is:

\[ \text{Number of Pickets} = \frac{\text{Fence Length (ft)} \times 12}{\text{Picket Width (in)} + \text{Picket Spacing (in)}} \]

The formula to arrange pickets in a parabolic shape is:

\[ \text{Height} = \text{Min Height} + (\text{Max Height} - \text{Min Height}) \times (1 - (2 \times \frac{i}{\text{Number of Pickets} - 1} - 1)^2) \]