If f(x) = ax^(2) + bx + c, how must a and b be related so that the graph of f(x-3)will be symmetric about the y-axis?

The book says to take -b/2a (x coordinate of f(x)). Since the new graph is 3 to the right, -b/2a = -3. So b = 6a.

My question is how do we know that the original f(x) is symmetrical about the y-axis???