I found these mathopenref tools extremely helpful in understanding graphs:
1. Linear Equations: http://www.mathopenref.com/linearexplorer.html
2. Quadratic Equations: http://www.mathopenref.com/quadraticexplorer.html
3. Cubic Equations: http://www.mathopenref.com/cubicexplorer.html
Things to do: Change the variable values with the help of the sliders and see the change in the shape of the curve.
For instance, in a quadratic equation y=ax^2+bx+c:
- changing c moves it up and down
- changing b changes the slope
- changing a alters the curvature of the parabolic element
Enjoy!