By reading the question, note that we want to describe the fact that a polynomial functions is symmetric about the y-axis. By symmetric, it means that the y-axis acts like a "mirror". That is, the right side of the graph looks exactly the same as the one on the left. This means that if we take one value for x, then the value of f(x) should be the same as if we take -x and calculate f(-x).
So
if f(x)=f(-x), then the graph of the polynomial function is symmetric about the y-axis.
That is the second option is the correct one.