When a is negative, the graph is reflected about the x-axis. For example, the parabola y=-x^2 has the same shape as y=x^2, but is pointing down instead of up.
Supposing V is a normed vector space, the p-norm of {\bf x} \in V is:
\lVert {\bf x} \rVert_p := \left(\sum_{i=1}^n |x|^p \right)^{\frac{1}{p}}
There are 3 special cases:
p= 2: Euclidean distance - 'as the crow flies'
p = 1: Taxicab distance - sum the absolute value of components...