find the coefficients a, b, and c of the quadratic polynomial. that passes through the three points (x, y)

Question

Sabrina Lozano 2022-4-12

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1694370-find-the-coefficients-a-b-and-c-of-the-quadratic-polynomial-that-passes-through-the-three-points

评论： Sabrina Lozano 2022-4-12

find the coefficients a, b, and c of the quadratic polynomial y = ax^2+ bx + c that passes through the three points (x, y) = (1, 4), (4, 73), (5, 120)

I am not sure how to go code this problem and need help!!

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

KSSV 2022-4-12

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1694370-find-the-coefficients-a-b-and-c-of-the-quadratic-polynomial-that-passes-through-the-three-points#answer_940750

在 MATLAB Online 中打开

% Convert the equation to form Ax = b 
P = [1, 4 ;4, 73; 5, 120] ;  % points 
x = P(:,1) ;   
y = P(:,2) ; 
b = P(:,2) ;  % RHS 
A = [x.^2 x repelem(1,3,1)] ;
% solve 
x = A\b ; 
% check 
A*x
ans = 3×1
    4.0000
   73.0000
  120.0000

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Sabrina Lozano 2022-4-12

What does the A=[x.^2 x repelem[(1,3,1)]; do?

请先登录，再进行评论。

Answer 2

KALYAN ACHARJYA 2022-4-12

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1694370-find-the-coefficients-a-b-and-c-of-the-quadratic-polynomial-that-passes-through-the-three-points#answer_940740

编辑：KALYAN ACHARJYA 2022-4-12

Sufficients Hints:

As it is the part of your work, please check the hints below, the equation is y = ax^2+ bx + c with three given Points.

Step 1:

Subsititute all those three points in the eqaution, you will get the three eqaution with unknown a,b,c

Step 2:

Create an Augumented Matrix using step 1 (3 equations)

Step 3:

Solve it for a,b,c

Helpful links

https://math.njit.edu/students/undergraduate/matlab_linear_systems.php

https://in.mathworks.com/help/matlab/ref/rref.html

Do it yourself is the best way of learning!

Hope it helps!

3 个评论
显示 1更早的评论隐藏 1更早的评论

Sabrina Lozano 2022-4-12

在 MATLAB Online 中打开

clc; close all;
A=[1 1 1 4;64 16 4 73;125 25 5 120]
rref(A)
ans =
    1.0000         0         0    0.2500
         0    1.0000         0    3.5000
         0         0    1.0000    0.2500
% would this be correct ??

Sabrina Lozano 2022-4-12

This code was for a cubic polynomial

请先登录，再进行评论。

Answer 3

VBBV 2022-4-12

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1694370-find-the-coefficients-a-b-and-c-of-the-quadratic-polynomial-that-passes-through-the-three-points#answer_940755

在 MATLAB Online 中打开

syms a b c

x = [1 4 5];

y = [4 73 120];

eqn = y == a*x.^2+b*x+c

eqn =

sol = solve(eqn,[a b c])

sol = struct with fields:

a: 6 b: -7 c: 5

4 个评论
显示 2更早的评论隐藏 2更早的评论

DGM 2022-4-12

You need to have the Symbolic Math toolbox to use syms.

Sabrina Lozano 2022-4-12

ah okay I only have the signal processing tool box.

请先登录，再进行评论。

Answer 4

Sam Chak 2022-4-12

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1694370-find-the-coefficients-a-b-and-c-of-the-quadratic-polynomial-that-passes-through-the-three-points#answer_940760

编辑：Sam Chak 2022-4-12

在 MATLAB Online 中打开

Hi @Sabrina Lozano

This problem can be rather easily solved with Curve-Fitting Toolbox with a click of a button or one simple function:

p = polyfit(x, y, 2)

However, I believe this is not the result your Professor wants to see. She or he probably wants to look at your efforts in computing the code according to what is taught in her or his lecture.

I'd suggest you to use a spreadsheet to tabulate out the necessary computations to be performed on the three points

Then, compose this:

which exactly a linear system

.

The solution is given by

which is easily computed in MATLAB without using the Curve-Fitting Toolbox

x = A\b

But you may lose some marks for not computing the inverse of matrix A manually that involves calculating the determinant. Better check with your Professor if computing the matrix inverse is necessary shown in the working.

Don't worry about being discovered by your Professor as these are merely guidelines from the textbook or public domain knowledge. You just have to compute the required items as shown above.

Hope this explanation is helpful for you to discover your learning experience as mentioned @KALYAN ACHARJYA.