The equation of a parabola with vertex at (0, 0) and axis of symmetry along the y-axis is of the form y = ax^2. The parabola passes through the point (-1, 1), so we can set up the following equation:
y = a * x^2
1 = a * (-1)^2
Solving for a, we get a = 1. Therefore, the equation of the parabola is y = x^2.