I´m working on an assignment which I think I have solved properly but since I don´t have the solution I´m a little nervous and I wonder if someone could take a look at it.

Here´s the question (translated from another language):

What is the best adjustment, in the "least square" sense, of the parabola to the data points given by the set

Here´s my solution:

I plug the given points in the equation and solve the system of linear equations and find that there is no solution . Which means i need to find a parabola which is as close as possible.

From where and

And since the columns in A are linearly independent, is invertible I get

Which gives me

This means that the parabola that is the best adjustment to the given set of points is

I really need to get this straight because I´m studying math on my own without the help of tutors and peers. So any help is appreciated.