Question

Find the parabola of the form y = ax^2 + b which best fits the points (1, 0), (2, 2), (3, 4) by minimizing the sum, S, of squares of the vertical distances from the above points to the parabola given by S = (a + b)^2 + (4a + b - 2)^2 + (9a + b - 4)^2. y = 2/7(3/7x^2-1) NOTE. You need to minimize S as a function of the variables a, b and then write the expression for y: y = ax^2 + b with a and b that you have found.

          Find the parabola of the form y = ax^2 + b which best fits the points (1, 0), (2, 2), (3, 4) by minimizing the sum, S, of squares of the vertical distances from the above points to the parabola given by

S = (a + b)^2 + (4a + b - 2)^2 + (9a + b - 4)^2.

y = 2/7(3/7x^2-1)

NOTE. You need to minimize S as a function of the variables a, b and then write the expression for y: y = ax^2 + b with a and b that you have found.

Find the parabola of the form y = ax^2 + b which best fits the points (1, 0), (2, 2), (3, 4) by minimizing the sum, S, of squares of the vertical distances from the above points to the parabola given by

S = (a + b)^2 + (4a + b - 2)^2 + (9a + b - 4)^2.

y = 2/7(3/7x^2-1)

NOTE. You need to minimize S as a function of the variables a, b and then write the expression for y: y = ax^2 + b with a and b that you have found.

Added by Mary V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

04/21/2023

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Find the parabola of the form y = ax^2 + b which best fits the points (1,0), (2,2), (3,4) by minimizing the sum, S, of squares of the vertical distances from the above points to the parabola given by S = (a + b)^2 + (4a + b - 2)^2 + (9a + b - 4)^2. y = (2/7)(3/7x^2 - 1) NOTE: You need to minimize S as a function of the variables a, b and then write the expression for y: y = ax^2 + b with a and b that you have found.