Un-editable curves in graph editor?

Question

Are the curves in the graph editor not supposed to be standard Beziers with standard editing techniques? I'm very good at controling Bezier curves in any application (including the pen tool in AE), but adjustment handles in the graph editor don't seem to follow the same rules.
For example: if the starting control point is set to ease out, it has an adjustment handle to the right, which I can move horizontally only. There isn't any way of dragging the adjustment handle at an angle, to change the shape of the curve controlled by the point. If I click the control point with the convert pen tool (including Alt + clicking) the curve changes to a straight line. Alt + clicking the curve again doesn't change it to a draggable curve point. It also doesn't seem possible to drag a control point or adjustment handle with the convert pen tool, which is how I'd normally get a second adjustment handle or change a line into a curve.
Creating points with the add pen tool also doesn't create control points that behave normally. The documentation makes no mention of any of this, and describes the curves as standard, editable Bezier paths. Everything else in AE CS4 seems to be working normally.
Anyone have an idea?

Answer 1

As Mylenium cleartly explained, the graph editor can display a value graph or a speed graph for any chosen property. By default the Graph Editor is set to auto-select which kind of graph to show for each property. In other words, it will pick the one that arguably it's the most useful in most cases. Since one could consider a motion path -the vector path you get in the Comp panel to represent position- as the most natural way of displaying position property values, the Graph Editor defaults to showing speed when you select position.
Now, having control over speed is a great thing. But many people are confused because these handles don't rotate like normal bèzier handles do. Don't worry: they do not rotate, simply because as far as speed goes, rotating the handles doesn't mean anything.
More info on this in AE Community help's section Controlling speed between keyframes.
Another head-scrather is that the traditional value graph for position is limited in that you can't use normal bèzier handles in it because the XYZ values are tied together. New in CS4m you now have the ability so separate dimensions, ie get separate properties for position x, position y and position z. When you do that, you get the same vector controls in the Graph Editor.
Take a look at Separate dimensions of Position to animate components individually in After Effects Community Help.