Fitted Model Line is looking very wrong. Fitting a Quadratic Regression Line to a plot

I am trying to plot a quadratic regression line over a plot.
This is the plot currently:

This is the code I have tried: I think it is quite self explanatory with the picture.

    model7<-lm(count~distance+I(distance^2), data=data)
summary(model7)

plot(count~distance, data=data)
lines(fitted(model7))

>Solution :

You could make a new dataframe and then add it to the plot as a line. Here is an example with ggplot2 instead of base R plots:

library(tidyverse)

#test data
set.seed(235)
data <- tibble(distance = sample(0:600, 30),
       count = (1e-6*distance-1e-5*(distance-300)^2 +1)+runif(30)) 

#model
model7<-lm(count~distance+I(distance^2), data=data)

#plot
ggplot(data, aes(distance, count))+
  geom_point()+
  geom_line(data = tibble(distance = seq(0,600, by = 1))|>
              (\(d) mutate(d, count = predict(model7, d)))())

Here is an update with Base R graphics:

#model line
fit_line <- data.frame(distance = seq(0,600, by = 1))
fit_line$count <- predict(model7, fit_line)

#plot
plot(count~distance, data=data)
lines(count~distance, data=fit_line)