Find the parabola of the form y = ax² + b which best fits the points (-1,0), (2, 2), (4,4) by minimizing the sum, S, of squares of the vertical distances from the above points to the parabola given by y = S = (a + b)² + (4a + b − 2)² + (16a+b− 4)². NOTE. You need to minimize S as a function of the variables a, b and then write the expression for y: y = ax² + b with a and b that you have found.
Find the parabola of the form y = ax² + b which best fits the points (-1,0), (2, 2), (4,4) by minimizing the sum, S, of squares of the vertical distances from the above points to the parabola given by y = S = (a + b)² + (4a + b − 2)² + (16a+b− 4)². NOTE. You need to minimize S as a function of the variables a, b and then write the expression for y: y = ax² + b with a and b that you have found.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Find the parabola of the form y = ax² + b which best fits the points (-1,0), (2, 2), (4,4) by minimizing the sum, S, of squares of the vertical distances from the
above points to the parabola given by
y =
S = (a + b)² + (4a + b − 2)² + (16a + b − 4)².
NOTE. You need to minimize S as a function of the variables a, b and then write the expression for y: y = ax² + b with a and b that you have found.
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Can you minimize the work because how to work the problem is cut out of the screen. So if you could make it smaller or rework the problem so that you can see all the steps that would be awesome. Thank you
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