How do you get the equation of polynomial regression using ggplot and R?

I've been trying to plot some data and add a third order polynomial trend line. I'm using the lm() and coef() functions to obtain a model for my data and then plot with ggplot.

Here is the relevant code:

Bytes is the name of my dependent variable (y). Resolution is the name of my independent variable (x).

model = lm(Bytes~poly(Resolution, 3), averaged_frame)
print(coef(model))

library(ggplot2)
plot = ggplot(averaged_frame, mapping = aes(x = Resolution, y = Bytes)) + 
  geom_point() + 
  stat_smooth(method="lm", formula = y~poly(x, 3), se = FALSE)

However, when I take the coefficients from print(coef(model)):

         (Intercept) poly(Resolution, 3)1 poly(Resolution, 3)2 poly(Resolution, 3)3 
           0.3392046            0.3686154            0.2504288            0.1274490 

And transpose them into a function:

f(x)=0.1274490x^3+0.2504288x^2+0.3686154x+0.3392046

And graph it, it looks completely different to the plot on ggplot.

I'm wondering what I am doing wrong here or how I might get an equation from the line in ggplot.

Here is an example with the ggpmisc package. This is for an order one regression, you have to adapt to your case.

df <- data.frame(x = c(1:100))
df$y <- 20 + 30 * df$x + rnorm(100, sd = 80)

library(ggpmisc)

my_formula <- y ~ x

myformat <- "y = %s + %s x --- R²: %s"
ggplot(df, aes(x, y)) + 
  geom_point() +
  geom_smooth(method = "lm", formula = my_formula, se = FALSE) +
  stat_poly_eq(
    formula = my_formula, output.type = "numeric",
    mapping = aes(
      label = 
        sprintf(
          myformat,
          formatC(after_stat(coef.ls)[[1]][[1, "Estimate"]]),
          formatC(after_stat(coef.ls)[[1]][[2, "Estimate"]]),
          formatC(stat(r.squared))),
    ),
    vstep = 0.1,
    size = 10
  )