Conic Sections are figures that can be formed by slicing a three dimensional right circular cone with a plane. There are different ways to do this, and each way yields a different figure. These figures can be represented on the graph as well as algebraically. The four conic sections are circles, ellipses, parabolas, and hyperbolas.
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Parabolas have directori.
McDonalds Arches
There are two ways of classifying parabolas: By the direction in which they are open: open at the top or at the bottom. By the number of real roots: 2 real, 1 real or no real roots.
The form is not specified in the question so it is hard to tell. But two parabolas with different vertices can certainly have the same axis of symmetry.