I think you need those unknowns in the priors. So I have a model like this:
brm(bf(y ~ a*x^2 + b*x + c, a + b + c ~ 1, nl = TRUE),
data = dat2, prior = prior2)
and prior2 looks like this
prior2 <- prior(normal(0,1), nlpar = "a") +
prior(normal(0, 2), nlpar = "b") +
prior(normal(0, 2), nlpar = "c")
Is that what you are talking about?