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.
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y=ax2