What are the key aspects of the graph of f(x)=x^2-b^2, where b is a real number

Think of  f(x)=x^2-b^2 as having the general form y = ax^2 + bx + cin this case, a=1, b=0 and c=-b^2.the x-coordinate of the vertex (and of the minimum value of f(x) would bex = -0 / (2*1) = 0.  the corresponding y-value would be -b^2, so that the vertex / minimum is at    (0,-b^2).  the graph opens up.