What are the key aspects of the graph of f(x) = x2 – b2, where b is a real number?

Given equation is [tex]f\left(x\right)=x^2-b^2[/tex].Now we need to find about what are the key aspects of the graph of [tex]f\left(x\right)=x^2-b^2[/tex], where b is a real number.We know that square of any number is always positive. then [tex]b^2[/tex] must be a positive number.So that means for any real number b, as the value of b increases then graph of f(x) shifts downward by [tex]b^2[/tex] units as compared to the graph of parent function [tex]f\left(x\right)=x^2[/tex]