To graph g(x) = -f(x - 1) + 2, we need to apply the following transformations to the graph of f(x) = x^2:
1. Shift the graph of f(x) to the right by 1 unit, which means replacing x with (x - 1) in the equation. This gives us: f(x - 1) = (x - 1)^2.
2. Reflect the graph of f(x - 1) about the x-axis by multiplying the expression by -1. This gives us: -f(x - 1) = -(x - 1)^2.
3. Shift the graph of -f(x - 1) up by 2 units. This gives us: g(x) = -f(x - 1) + 2 = -(x - 1)^2 + 2.
Therefore, the graph of g(x) is a downward-facing parabola that has been shifted 1 unit to the right and 2 units up from the graph of f(x) = x^2.