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

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Sabrina Lozano on 12 Apr 2022
Commented: Sabrina Lozano on 12 Apr 2022
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!!
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### Answers (4)

KSSV on 12 Apr 2022
% 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
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Sabrina Lozano on 12 Apr 2022
What does the A=[x.^2 x repelem[(1,3,1)]; do?

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KALYAN ACHARJYA on 12 Apr 2022
Edited: KALYAN ACHARJYA on 12 Apr 2022
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
Do it yourself is the best way of learning!
Hope it helps!
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Sabrina Lozano on 12 Apr 2022
This code was for a cubic polynomial

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VBBV on 12 Apr 2022
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
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Sabrina Lozano on 12 Apr 2022
ah okay I only have the signal processing tool box.

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Sam Chak on 12 Apr 2022
Edited: Sam Chak on 12 Apr 2022
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.
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Sabrina Lozano on 12 Apr 2022
Thank you very much this explanation was very helpfull !!! This is my fisrt class using matlab im still tryin to learn the basics!

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