Least square quad. lines of fit: Xk(2 1 0 1 2) Yk(5.8 1.1 3.8 3.5 1.5)

[Mecoo]

Find the least-square parabola f(x) = Ax2+Bx+C for each set of data.

Xk(2 1 0 1 2)
Yk(5.8 1.1 3.8 3.5 1.5)

Xk(2 1 0 1 2)
Yk(2.8 2.1 3.25 6.0 11.5)

Xk(2 1 0 1 2)
Yk(10 1 0 2 9)



Pls help solve

 

[tkhunny]

Let's see your best efforts.

If it were me, I'd look into "Normal Equations" and solve the resulting System for the desired parameters.

 

[HallsofIvy]

Do you know what "least square" means here?

For the first problem, Xk(2 1 0 1 2), Yk(5.8 1.1 3.8 3.5 1.5)
With y= Ax^2+ Bx+ C, y(2)= 4A+ 2B+ C but y= 5.8 so the "error" is 4A+ 2B+ C- 5.8 and the "square error is (4A+ 2B+ C- 5.8)^2. Do that for each of the others and add them to get the "sum of squares". Find A, B, and C to minimize that sum of squares.

 

[stapel]

Find the least-square parabola f(x) = Ax2+Bx+C for each set of data.

Xk(2 1 0 1 2)
Yk(5.8 1.1 3.8 3.5 1.5)

Xk(2 1 0 1 2)
Yk(2.8 2.1 3.25 6.0 11.5)

Xk(2 1 0 1 2)
Yk(10 1 0 2 9)

Pls help solve

They told you in class what buttons to push on your graphing calculator. You've verified the steps in your owner's manual. Where are you stuck?

Please be specific. Thank you!