Mixing
Quadratic equation formula for a,b,c from 3 points
$begingroup$
I can solve for a, b, c given three points for a parabola for example (1,1)(2,4)(3,9) but i need to create a program which returns a,b,c in the form:
y = ax^2 + bx + c
What is a formula that will find out a, b, c? Someone on another forum mentioned Lagrange but being a high school student i don't know much about Uni level physics. Also i can work with matrices if anyone has a matrix formula - but please explain your formulas as to why it works!
Any help appreciated!
Thanks,
Itechmatrix
algorithms quadratics quadratic-programming
asked Dec 2 '14 at 3:05
user24492user24492
1
$endgroup$
add a comment |
$begingroup$
I can solve for a, b, c given three points for a parabola for example (1,1)(2,4)(3,9) but i need to create a program which returns a,b,c in the form:
y = ax^2 + bx + c
What is a formula that will find out a, b, c? Someone on another forum mentioned Lagrange but being a high school student i don't know much about Uni level physics. Also i can work with matrices if anyone has a matrix formula - but please explain your formulas as to why it works!
Any help appreciated!
Thanks,
Itechmatrix
algorithms quadratics quadratic-programming
asked Dec 2 '14 at 3:05
user24492user24492
1
$endgroup$
$begingroup$
See:-physicsforums.com/threads/…
$endgroup$
– Mick
Dec 2 '14 at 4:21
$begingroup$
@Mick I can't find a working formula on those pages?
$endgroup$
– user24492
Dec 2 '14 at 5:44
$begingroup$
Look for Xitami’s reply. The post also provides a link explaining how to find the inverse of a matrix. Also, @JoeTaxpayer has also included a method (namely Cramer’s rule) to find the solution of that matrix.
$endgroup$
– Mick
Dec 2 '14 at 14:30
add a comment |
$begingroup$
I can solve for a, b, c given three points for a parabola for example (1,1)(2,4)(3,9) but i need to create a program which returns a,b,c in the form:
y = ax^2 + bx + c
What is a formula that will find out a, b, c? Someone on another forum mentioned Lagrange but being a high school student i don't know much about Uni level physics. Also i can work with matrices if anyone has a matrix formula - but please explain your formulas as to why it works!
Any help appreciated!
Thanks,
Itechmatrix
algorithms quadratics quadratic-programming
asked Dec 2 '14 at 3:05
user24492user24492
1
$endgroup$
I can solve for a, b, c given three points for a parabola for example (1,1)(2,4)(3,9) but i need to create a program which returns a,b,c in the form:
y = ax^2 + bx + c
What is a formula that will find out a, b, c? Someone on another forum mentioned Lagrange but being a high school student i don't know much about Uni level physics. Also i can work with matrices if anyone has a matrix formula - but please explain your formulas as to why it works!
Any help appreciated!
Thanks,
Itechmatrix
algorithms quadratics quadratic-programming
algorithms quadratics quadratic-programming
asked Dec 2 '14 at 3:05
user24492user24492
1
asked Dec 2 '14 at 3:05
user24492user24492
1
edited Dec 2 '14 at 3:10
user24492
asked Dec 2 '14 at 3:05
user24492user24492
1
asked Dec 2 '14 at 3:05
user24492user24492
1
asked Dec 2 '14 at 3:05
user24492user24492
1
1
$begingroup$
See:-physicsforums.com/threads/…
$endgroup$
– Mick
Dec 2 '14 at 4:21
$begingroup$
@Mick I can't find a working formula on those pages?
$endgroup$
– user24492
Dec 2 '14 at 5:44
$begingroup$
Look for Xitami’s reply. The post also provides a link explaining how to find the inverse of a matrix. Also, @JoeTaxpayer has also included a method (namely Cramer’s rule) to find the solution of that matrix.
$endgroup$
– Mick
Dec 2 '14 at 14:30
add a comment |
$begingroup$
See:-physicsforums.com/threads/…
$endgroup$
– Mick
Dec 2 '14 at 4:21
$begingroup$
@Mick I can't find a working formula on those pages?
$endgroup$
– user24492
Dec 2 '14 at 5:44
$begingroup$
Look for Xitami’s reply. The post also provides a link explaining how to find the inverse of a matrix. Also, @JoeTaxpayer has also included a method (namely Cramer’s rule) to find the solution of that matrix.
$endgroup$
– Mick
Dec 2 '14 at 14:30
$begingroup$
See:-physicsforums.com/threads/…
$endgroup$
– Mick
Dec 2 '14 at 4:21
$begingroup$
See:-physicsforums.com/threads/…
$endgroup$
– Mick
Dec 2 '14 at 4:21
$begingroup$
@Mick I can't find a working formula on those pages?
$endgroup$
– user24492
Dec 2 '14 at 5:44
$begingroup$
@Mick I can't find a working formula on those pages?
$endgroup$
– user24492
Dec 2 '14 at 5:44
$begingroup$
Look for Xitami’s reply. The post also provides a link explaining how to find the inverse of a matrix. Also, @JoeTaxpayer has also included a method (namely Cramer’s rule) to find the solution of that matrix.
$endgroup$
– Mick
Dec 2 '14 at 14:30
$begingroup$
Look for Xitami’s reply. The post also provides a link explaining how to find the inverse of a matrix. Also, @JoeTaxpayer has also included a method (namely Cramer’s rule) to find the solution of that matrix.
$endgroup$
– Mick
Dec 2 '14 at 14:30
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
When you plug in the three points, you have three equations in three unknowns, where the unknowns are A,B,and C. Use matrix arithmetic to solve via simple program.
By Matrix, I mean using Cramer's rule.
answered Dec 2 '14 at 3:27
JoeTaxpayerJoeTaxpayer
2,20121326
$endgroup$
$begingroup$
Matrix Arithmetic? Could you please elaborate on that @JoeTaxpayer?
$endgroup$
– user24492
Dec 2 '14 at 3:34
$begingroup$
I edited my answer.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 12:36
$begingroup$
To make things a bit easier, I think the roles of a and x (also b vs y and c vs z) should be interchanged instead. This is because the values of a, b, c are the required.
$endgroup$
– Mick
Dec 2 '14 at 14:27
$begingroup$
@Mick - When working with my students I make an effort to help them not get hooked on the variable designations. I was clear in the answer I posted that OP need to be aware of that.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 14:32
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
When you plug in the three points, you have three equations in three unknowns, where the unknowns are A,B,and C. Use matrix arithmetic to solve via simple program.
By Matrix, I mean using Cramer's rule.
answered Dec 2 '14 at 3:27
JoeTaxpayerJoeTaxpayer
2,20121326
$endgroup$
$begingroup$
Matrix Arithmetic? Could you please elaborate on that @JoeTaxpayer?
$endgroup$
– user24492
Dec 2 '14 at 3:34
$begingroup$
I edited my answer.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 12:36
$begingroup$
To make things a bit easier, I think the roles of a and x (also b vs y and c vs z) should be interchanged instead. This is because the values of a, b, c are the required.
$endgroup$
– Mick
Dec 2 '14 at 14:27
$begingroup$
@Mick - When working with my students I make an effort to help them not get hooked on the variable designations. I was clear in the answer I posted that OP need to be aware of that.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 14:32
add a comment |
$begingroup$
When you plug in the three points, you have three equations in three unknowns, where the unknowns are A,B,and C. Use matrix arithmetic to solve via simple program.
By Matrix, I mean using Cramer's rule.
answered Dec 2 '14 at 3:27
JoeTaxpayerJoeTaxpayer
2,20121326
$endgroup$
$begingroup$
Matrix Arithmetic? Could you please elaborate on that @JoeTaxpayer?
$endgroup$
– user24492
Dec 2 '14 at 3:34
$begingroup$
I edited my answer.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 12:36
$begingroup$
To make things a bit easier, I think the roles of a and x (also b vs y and c vs z) should be interchanged instead. This is because the values of a, b, c are the required.
$endgroup$
– Mick
Dec 2 '14 at 14:27
$begingroup$
@Mick - When working with my students I make an effort to help them not get hooked on the variable designations. I was clear in the answer I posted that OP need to be aware of that.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 14:32
add a comment |
$begingroup$
When you plug in the three points, you have three equations in three unknowns, where the unknowns are A,B,and C. Use matrix arithmetic to solve via simple program.
By Matrix, I mean using Cramer's rule.
answered Dec 2 '14 at 3:27
JoeTaxpayerJoeTaxpayer
2,20121326
$endgroup$
When you plug in the three points, you have three equations in three unknowns, where the unknowns are A,B,and C. Use matrix arithmetic to solve via simple program.
By Matrix, I mean using Cramer's rule.
answered Dec 2 '14 at 3:27
JoeTaxpayerJoeTaxpayer
2,20121326
edited Dec 2 '14 at 12:35
answered Dec 2 '14 at 3:27
JoeTaxpayerJoeTaxpayer
2,20121326
answered Dec 2 '14 at 3:27
JoeTaxpayerJoeTaxpayer
2,20121326
answered Dec 2 '14 at 3:27
JoeTaxpayerJoeTaxpayer
2,20121326
2,20121326
$begingroup$
Matrix Arithmetic? Could you please elaborate on that @JoeTaxpayer?
$endgroup$
– user24492
Dec 2 '14 at 3:34
$begingroup$
I edited my answer.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 12:36
$begingroup$
To make things a bit easier, I think the roles of a and x (also b vs y and c vs z) should be interchanged instead. This is because the values of a, b, c are the required.
$endgroup$
– Mick
Dec 2 '14 at 14:27
$begingroup$
@Mick - When working with my students I make an effort to help them not get hooked on the variable designations. I was clear in the answer I posted that OP need to be aware of that.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 14:32
add a comment |
$begingroup$
Matrix Arithmetic? Could you please elaborate on that @JoeTaxpayer?
$endgroup$
– user24492
Dec 2 '14 at 3:34
$begingroup$
I edited my answer.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 12:36
$begingroup$
To make things a bit easier, I think the roles of a and x (also b vs y and c vs z) should be interchanged instead. This is because the values of a, b, c are the required.
$endgroup$
– Mick
Dec 2 '14 at 14:27
$begingroup$
@Mick - When working with my students I make an effort to help them not get hooked on the variable designations. I was clear in the answer I posted that OP need to be aware of that.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 14:32
$begingroup$
Matrix Arithmetic? Could you please elaborate on that @JoeTaxpayer?
$endgroup$
– user24492
Dec 2 '14 at 3:34
$begingroup$
Matrix Arithmetic? Could you please elaborate on that @JoeTaxpayer?
$endgroup$
– user24492
Dec 2 '14 at 3:34
$begingroup$
I edited my answer.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 12:36
$begingroup$
I edited my answer.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 12:36
$begingroup$
To make things a bit easier, I think the roles of a and x (also b vs y and c vs z) should be interchanged instead. This is because the values of a, b, c are the required.
$endgroup$
– Mick
Dec 2 '14 at 14:27
$begingroup$
To make things a bit easier, I think the roles of a and x (also b vs y and c vs z) should be interchanged instead. This is because the values of a, b, c are the required.
$endgroup$
– Mick
Dec 2 '14 at 14:27
$begingroup$
@Mick - When working with my students I make an effort to help them not get hooked on the variable designations. I was clear in the answer I posted that OP need to be aware of that.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 14:32
$begingroup$
@Mick - When working with my students I make an effort to help them not get hooked on the variable designations. I was clear in the answer I posted that OP need to be aware of that.
$endgroup$
– JoeTaxpayer
Dec 2 '14 at 14:32
add a comment |
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$begingroup$
See:-physicsforums.com/threads/…
$endgroup$
– Mick
Dec 2 '14 at 4:21
$begingroup$
@Mick I can't find a working formula on those pages?
$endgroup$
– user24492
Dec 2 '14 at 5:44
$begingroup$
Look for Xitami’s reply. The post also provides a link explaining how to find the inverse of a matrix. Also, @JoeTaxpayer has also included a method (namely Cramer’s rule) to find the solution of that matrix.
$endgroup$
– Mick
Dec 2 '14 at 14:30