Beziers in Graph Editor

The curve option in the graph editor changes depending on the properties and whether you are editing the Speed Graph or the Value Graph. If you are editing a property with an array like Position or Effect/Turbulent Displace/Transform/Offset Turbulence, you have to switch to the Speed Graph to get bezier control handles on the speed of the change. The Bezier handles you get for a property with an array are more accurately described as acceleration handles. Drag them left or right to change the acceleration curve. 

If you want to create a curve in a Path that has two or more properties you have to use the Layer Panel to adjust that motion curve. Only Layer/Transform/Position has a curve you can edit in the Composition Panel.

This is what that looks like:

Maybe this tutorial I produced will help you figure out the Graph Editor.