Match the graph to its equation.

The first graph is a downward-opening parabola with its vertex at approximately (1, 2). The equation $$y = -3x^2 + 3x + 1$$ represents a downward-opening parabola. Its vertex can be found at $$x = -b/(2a) = -3/(2*(-3)) = 0.5$$. Substituting $$x=0.5$$ into the equation gives $$y = -3(0.5)^2 + 3(0.5) + 1 = -3(0.25) + 1.5 + 1 = -0.75 + 1.5 + 1 = 1.75$$. This vertex (0.5, 1.75) closely matches the graph. The other equations represent upward-opening parabolas or have vertices that do not match the graph.