Best way to graph a regression??

First, the best way to get help is to provide a reproducible example [reprex]; there are references for how to do it in the help here in the RStudio community. FAQ: What's a reproducible example (`reprex`) and how do I create one?

Second, I am pretty sure the problem is the lm call. Try modifying your lm to use the formula and data form.

mod = lm(Life.expectancy ~ poly(Adult.Mortality, 2), data=D)

You may also need to name the input, so alter the definition of x4

x4 = data.frame(Adult.Mortality = seq(min(D$Adult.Mortality), max(D$Adult.Mortality),

And remove the duplicate data.frame() call.

y4 = predict(mod, x4, interval = "confidence")

That should fix it.