Mean response: it’s the inference interval for E(Y(x)) = B0+B1x+B2x^2
My understanding is, mean response interval is the interval for the estimate mean. It indicates the probability that the mean is in the interval
Prediction interval: it’s the inference interval Y(x) = B0+B1x+B2x^2+epsilon
is the interval for prediction the real data or population. So it will have the wider range.