If we are given 
to analyze, the standard equation looks like a parabola with a vertex at point (0,0).
Changing a does not rid the equation of its (0,0) vertex or of its parabolic shape. If a is a positive value, then the graph opens upward, but if a is negative the graph opens downward.
We can see that as the absolute value of a gets larger, the graph gets closer to the the vertical axis. As the absolute value of a gets smaller, the graph moves away from the vertical axis.
It should also be noted that the graphs continue in an infinite direction. In other words, for the graph if a is 1, then the x values and the y values will never stop. The graph does not have an ending point; the y values will continue into positive infinity.
But, as you can see from the diagram, the x values do not increase as quickly as the y values. For example, the graph 
moves from point (2,4) to (4,16); the x value increased by only 2, yet the y value increased by 12.