As a quick suggestion for conic sections - if you can complete the square for an equation in general form...... I would suggest making a quick sketch of the graph using the coordinates of the center (or turning point) and then plot your major points from there.

Also, a good note for parabolas is that the graph should always look to "eat" the focus. So when you find the turning point and draw a rough sketch of a parabola- the focus should be inside of the figure.