Yes, but a parabola, itself, can have only a vertical line of symmetry.
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No, a shape is more technically referred to as a polygon. Some examples of polygons include squares and triangles. Polygons cannot have curved sides so therefore a parabola is not a polygon nor a shape. A parabola is a line, it extends in the direction it is going for infinity.
A parabola is not a shape, it is actually a curved line in a coordinate plane. It is shaped like a U turned in any direction. The two basic equations for it are y=a(x-h)2+k or x=a(y-k)2+h.
A parabola is a curved shape that is plotted on the Cartesian plane.
Yes
It is a function because for every point on the horizontal axis, the parabola identified one and only one point in the vertical direction.