library(plotly)
library(dplyr)

Non_Lin_Regressie <- function(x,y){
  # Solving the least squares method
  Pol_Matrix          <-    matrix(c(x^2,x,rep(1,length(x))),ncol=3)
  LHS_pol             <-    t(Pol_Matrix) %*% Pol_Matrix            # Computes the LHS
  RHS_pol             <-    t(Pol_Matrix) %*% y                     # Computes the RHS
  x_sol_pol           <-    solve(LHS_pol,RHS_pol)                  # Solves the equation
  return(x_sol_pol)
}

x <- c(-1,-1/2,0,1/2,1)
y<- c(2,1,0,1,2)
sol <- Non_Lin_Regressie(x,y)
func <- sol[1]*x^2 + sol[2]*x+sol[3]
plot_ly(x=~x, mode= 'lines') %>%
  add_trace(y = ~func, line = list(shape = "spline"), name= 'solved by LS') %>%
  add_trace(y=~y, name= 'normal plot')

[,1]
[1,] 1.7142857
[2,] 0.0000000
[3,] 0.3428571