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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