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

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!!

Answer 1

[KSSV]

% 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

[Sabrina Lozano]

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

Answer 2

[KALYAN ACHARJYA]

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!

[Sabrina Lozano]

The links were helpful thank you!!

[Sabrina Lozano]

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]

This code was for a cubic polynomial

Answer 3

[VBBV]

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

[Sabrina Lozano]

Very simple straight forward code very helpfull seeing how it was structured!

[Sabrina Lozano]

it seems that the syms a b c is undefined when I tested the code with a similar porblem ?

[DGM]

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

[Sabrina Lozano]

ah okay I only have the signal processing tool box.

Answer 4

[Sam Chak]

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.

[Sabrina Lozano]

Thank you very much this explanation was very helpfull !!! This is my fisrt class using matlab im still tryin to learn the basics!