model <- function(par, x){
   n <- length(x)
   res <- rep(0,n)
   for(i in 1:n){
      A0 <- par[3] + (par[4]-par[1])*par[6] + (par[5]-par[2])*par[6]^2
      if(x[i] <= par[6]){
         res[i] <- A0 + par[1]*x[i] + par[2]*x[i]^2
      }else{
         res[i] <- par[3] + par[4]*x[i] +par[5]*x[i]^2
      }
   }
   return(res)
 }

sum_squares <- function(par, x, y){
    ss <- sum((y-model(par,x))^2)
    return(ss)
 }

#I found these initial values with a few minutes of guess and check.
 par0 <- c(7,-1,-395,70,-2.3,10)
 sol <- optim(par= par0, fn=sqerror, x=x, y=y)$par