Animation of

y=ax2

This is the graph of y=ax2. In this particular example, the range of a is -100 to 100. Obviously a can be infinitely large or small.

Notice that as the value of a increases (approaches infinity), the parabola is contained to quadrants I and II and gets increasingly closer to the x-axis. As the value of a decreases (approaches negative infinity), the parabola still approaches the x-axis, but is contained to quadrants III and IV.

y=ax2