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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 13T
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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.
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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