Definition of function periodicity: If t is a non-zero constant, let f(x)=f(x+T) be a constant for any x in the definition field, then f(x) is called a periodic function and t is called the period of the function.
Symmetry is about y axis symmetry, about a line symmetry,
Quadratic function is symmetric about symmetry.
Symmetry axis is
Sine and cosine functions also have symmetry axes. It is also a periodic function.