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

92 次查看（过去 30 天）
Sabrina Lozano
Sabrina Lozano 2022-4-12
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!!

请先登录，再回答此问题。

回答（4 个）

KSSV
KSSV 2022-4-12
Ran in:
% 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
KALYAN ACHARJYA
KALYAN ACHARJYA 2022-4-12
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
Sabrina Lozano
Sabrina Lozano 2022-4-12
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 ??

请先登录，再进行评论。

VBBV
VBBV 2022-4-12
Ran in:
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

请先登录，再进行评论。

Sam Chak
Sam Chak 2022-4-12
编辑：Sam Chak 2022-4-12
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.

类别

在 Help Center 和 File Exchange 中查找有关 Number Theory 的更多信息

标签

产品


版本

R2021b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by