We mostly looked at hyperbolas.
For the equations, one term (x or y squared) is positive and the other is negative. The graph will be either vertical for positive y or horizontal for positive x.
h,k are the center. The asymptotes will go through the center.
Sometimes associating something with an image can help. I thought of b/a corresponding with the letter b and being horizontal.
For factoring cubic equations, if you have one zero, you can divide using that information and then get to a quadratic function.