How to compensate the flipped coordinate system of core graphics for easy drawing?

Problem: Origin is at lower-left corner; positive y goes upward (negative y goes downward).
Goal: Origin at upper-left corner; positive y going downward (negative y going upward).

Solution:

1. Move origin up by the view’s height.
2. Negate (multiply by -1) the y axis.

The way to do this in code is to translate up by the view bounds’ height and scale by (1, -1), in that order.

There are a couple of portions of the Quartz 2D Programming Guide that are relevant to this topic, including “Drawing to a Graphics Context on iPhone OS” and the whole chapter on Transforms. Of course, you really should read the whole thing.