F(x) = a(x - h)power of 3 + k    describe what a, h and k do within our function. 

F(x) = a(x - h)³ + k

The parent graph is F(x) = x³

k - shifts the parent graph up k-units (or down if it is negative).  This is also called a vertical shift.

h - shifts the parent graph to the right h-units (or left if it is negative).  This is also called a horizontal shift.

a - stretches the parent graph vertically by a factor of "a"

Additonally, the coordinate (h, k) is the center/vertex of the graph.