Suppose we have a set of data points $(x_1,y_1),(x_2,y_2),$dots,$(x_n,y_n)$ and the regression model is defined as

$y={}_0+{}_1+{}_{2x2}.$ Derive the expressions for the coefficients ${}_0,{}_1,$ and ${}_2$ that minimize the sum of

squared errors $($SSE$)$ for this quadratic regression model.