The expression x^2 - 9 is a quadratic polynomial, which is a type of mathematical expression that includes a variable raised to the second power. In this case, x is the variable, and the expression can be factored into (x - 3)(x + 3). This means that the expression equals zero when x is either 3 or -3, which are known as the roots or solutions of the equation. The graph of y = x^2 - 9 is a parabola that opens upwards. The vertex of this parabola is located at the point (0, -9), which is the lowest point on the graph. The expression is also related to the concept of difference of squares, as it can be rewritten as x^2 - 3^2. This relationship helps in understanding how to solve equations involving this polynomial.