Science:Math Exam Resources/Courses/MATH221/December 2009/Question 09
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Question 09 

Find the least square fit of a parabola to the data

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Science:Math Exam Resources/Courses/MATH221/December 2009/Question 09/Hint 1 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. First we can build a subVandermonde matrix, even though we know that this matrix probably won’t fit all the points Since we have 4 points and we want a parabola, the dimension of the subVandermonde matrix would be 4 x 3
Since we want to find the least square, we would like to solve the equation for where
The system then becomes
Solve the equation to get
So the parabola is 