Simple linear algebra refresher?

[medinaj2160]

Homework Statement

Given the three x-values {-1,1,2} and the corresponding y-values {-1,1,8}, write down the three equations that define the quadratic polynomial that interpolates this data.

I have completely forgot how to do this.

Thanks

Homework Equations

IDK y=mx+b

The Attempt at a Solution

none, I already have taken calculus 1-3 and de, and I cannot remember how to do this :(

 

[Hurkyl]

Before worrying about how to do the question, try first stating what the question is, symbolically.

 

[medinaj2160]

Before worrying about how to do the question, try first stating what the question is, symbolically.

Like I said I don't remember anything my brain is fried for some reason.

Looking at the data I just know that they are points
(-1,-1) (1,1) (2,8)

I got

-1=a-b+c
1=a+b+c
8=4a+2b+c

?

 

[Hurkyl]

From the latest post, I suspect you've remembered a lot more than you let on -- just to double check, can you say what a, b, and c are, and how they relate to the quadratic interpolating polynomial you're trying to find?



So anyways -- you've reduced the problem to "How do I solve a system of three linear equations in three unknown variables?" right? And there's nothing else to it?

 

[medinaj2160]

From the latest post, I suspect you've remembered a lot more than you let on -- just to double check, can you say what a, b, and c are, and how they relate to the quadratic interpolating polynomial you're trying to find?



So anyways -- you've reduced the problem to "How do I solve a system of three linear equations in three unknown variables?" right? And there's nothing else to it?

I solve for a, b, c using the solver I got 6, 1, -6

So I guess the quadratic polynomial that interpolates the data is f(x)= 6x^2+Y-6, correct?

Part 2)
Write down the matrix equation whose solution is the vector of coefficients of the interpolating polynomial.

In this part, is he asking for the 3X3 matrix of the 3 equations?
a=[1 -1 1; 1 1 1; 2 2 1] b=[-1 1 8]
where
a*X=b

 

[Mark44]

Hurkyl's asking you what a, b, and c represent (not their values) in terms of the interpolating quadratic.

 

[medinaj2160]

Hurkyl's asking you what a, b, and c represent (not their values) in terms of the interpolating quadratic.

the values in which the interpolation will take place?

 

[Mark44]

No - what is the interpolating polynomial you are using?

 

[medinaj2160]

No - what is the interpolating polynomial you are using?

Is this one f(x)= 6x^2+Y-6