To graph the function f(x) = -x^2 - 2x + 1, we first need to find the vertex and the axis of symmetry. The vertex can be calculated using the formula x = -b/(2a), where a and b are the coefficients from the quadratic equation. Here, a = -1 and b = -2, leading to x = 1. Substituting x = 1 back into the function gives us the y-coordinate of the vertex, which is -2. Therefore, the vertex is (1, -2). The axis of symmetry is a vertical line that passes through the vertex, which is x = 1. To graph the function, we plot the vertex and find additional points by substituting other x-values into the function. For example, f(0) = 1 gives us the point (0, 1), and f(2) = -9 gives us (2, -9). The graph will be a downward-opening parabola with the vertex at (1, -2) and the axis of symmetry at x = 1.