To determine which graph matches the function f(x)=2x^3-2x^2-8x+8, we analyze the characteristics of the cubic function. The degree of the polynomial is 3, indicating it is a cubic function, which typically has one maximum or minimum point. The leading coefficient is positive, suggesting the graph will start in the bottom left and end in the top right. The constant term is 8, meaning the graph crosses the y-axis at (0,8). The negative coefficient of the quadratic term indicates the presence of a maximum point. We can find the x-coordinate of this maximum using the formula x=-b/(2a), which gives us x=0.5. Plugging this value back into the function, we find the y-coordinate of the maximum point to be 6, resulting in the point (0.5,6). By comparing these characteristics with the available graphs, we can eliminate those that do not meet these criteria, ultimately identifying the correct graph.