Linear Algebra A certain experiment1 produces the data point

Linear Algebra:

A certain experiment1 produces the data points (1; 1:6), (2; 2:5), (3; 3:3), (4; 3:7), and (5; 3:9).
Describe the model that produces a least-squares fit of these points by a function of the form
y = c1x + c2x2

Solution

This is difficult to show all the steps here

I used R statisitical software for compution of this model

I have a data points

(1,6), (2,5), (3,3) ,(3,7), (3,9)

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The quadrtic regresion equation is

y= 9.33 - 4.5x +1.1667x^2