Given the function $f(x) = x^2 - 1$, here are a few important details about it:

1. Type of Function: This is a quadratic function, which generally has the form $f(x) = ax^2 + bx + c$. In your case, $a = 1$, $b = 0$, and $c = -1$.

2. Vertex: The vertex of the parabola described