How to deal with a quadratic model that has too many fitted values?

I'm trying to fit a quadratic regression model to a dataset and then plot the curve on a scatterplot. The dataset is about number of episodes and screentime for characters in a TV show.

I plotted a scatterplot with episodes on x axis and screentime on y axis this worked fine.

Then I create the model as follows:

model <- lm(screentime~episodes+I(episodes^2), data = got)
lines(fitted(model))

This gives me a model with correct coeefficients however there are too many fitted.values, I assume due to the fact that some characters have the same number of episodes this leads to the lines not being plotted fully.