The expression x^2 - 1 is a quadratic polynomial, which means it is a mathematical expression of the form ax^2 + bx + c. In this case, a = 1, b = 0, and c = -1. This polynomial can be factored into (x - 1)(x + 1), showing that it has roots at x = 1 and x = -1. The graph of y = x^2 - 1 is a parabola that opens upwards, with its vertex located at the point (0, -1). The expression is often used in algebra and calculus to illustrate concepts such as factoring, finding roots, and analyzing the behavior of quadratic functions.