The effects of changing q in y=a(x-p +q

If q is increased, the parabola translates up the y-axis and if q is decreased, the parabola is translated down.

The effect of changing p

If p has a positive sign, the parabola moves left on the x-axis, and if it is negative, the parabola moves right.

The effect of changing a

the smaller a gets, the wider the parabola, the larger a gets, the slimmer the parabola. a also dictates weather or not the parabola opens down or opens up. If a is negative, the parabola opens down and it has a maximum, but if a is positive, the parabola opens up, and it has a minimum.

This formula also tells you the vertex. you use p and q to find the vertex. For example, if you had y=2(x-3+5, the vertex would be at (3,5) (if it were +3, the vertex would be (-3,5).