When I plug the values of x into the equation you wrote I get:
which is a lot closer than your calculation woudl indicate. I don't know why your calculator is giving you answers that are so far off - but I'm guessing that yuo may have used 4.6713 instead of 4.6717 for the third coefficient.
Also, consider how you have rounded off the coefficients, especially the second one which is good to only three signficant digits (0.0409). Given this rounding the result can be expected to be accurate to only three significant digits as well. If you want more accuracy you need to provide more digits. Try:
y = 0.0001x^3 - 0.0408958x^2 + 4.671667x + 280.32