Final answer:
A cubic curve can have symmetry about the y-axis, symmetry about the x-axis, and rotational symmetry about the origin.
Step-by-step explanation:
A cubic curve can have Symmetry about the y-axis, Symmetry about the x-axis, and Rotational symmetry about the origin.
Symmetry about the y-axis: If a cubic curve has symmetry about the y-axis, it means that if you fold the curve along the y-axis, the two halves will overlap exactly. An example of a cubic curve with symmetry about the y-axis is y = x3.
Symmetry about the x-axis: If a cubic curve has symmetry about the x-axis, it means that if you rotate the curve 180 degrees around the x-axis, it will still look the same. An example of a cubic curve with symmetry about the x-axis is y = -x3.
Rotational symmetry about the origin: If a cubic curve has rotational symmetry about the origin, it means that if you rotate the curve 180 degrees around the origin, it will still look the same. An example of a cubic curve with rotational symmetry is y = x3.