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.
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A parabola is a curved shape that is plotted on the Cartesian plane.
Yes
Yes, but a parabola, itself, can have only a vertical line of symmetry.
The parabola shape is magnified. If you keep the same scale for the graph, the parabola will look wider, more flattened out.
They both have an arc shape.