What is "what are the key aspects of the graph of f(x) = x2 – b2?

The graph of the function f(x) = x^2 - b^2 is a parabola.

The key aspects of this graph include:

1. Vertex: The vertex of the parabola is at (0,-b^2). The vertex is the lowest point on the graph if b is positive, and is the highest point on the graph if b is negative.

2. Axis of Symmetry: The axis of symmetry of the parabola is the vertical line x = 0. This means that the parabola is symmetric with respect to this line.

3. Vertex Form: The function f(x) = x^2 - b^2 can also be written as f(x) = (x - 0)^2 - b^2. This is in vertex form where the vertex is (0,-b^2) and the axis of symmetry is x = 0.

4. Shape: The graph of f(x) = x^2 - b^2 opens upwards if b is positive and opens downwards if b is negative.

5. Intercepts: The y-intercept occurs when x = 0, so the y-intercept is f(0) = -b^2. There are no x-intercepts for this graph since it is a parabola that does not intersect the x-axis.

Overall, the key aspects of the graph of f(x) = x^2 - b^2 include the vertex, axis of symmetry, vertex form, shape, and intercepts.