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

Answer:

The graph of f(x) = x^2 – b^2 is a parabola that opens upward. Its x-intercepts are at b and –b, meaning it has opposite x-intercepts. The y-intercept is located at (0, –b^2), which also serves as the vertex of the parabola. Since the vertex is on the y-axis, the graph is symmetrical about the y-axis.