Coefficients of a quadratic equation + Matrices

[MagdaLena]

i have an task:
find a,b and c in the quadratic equation f(x) = ax^(2) +bx +c
which pass through the points : P(1,6), Q(-1,8) and R(2,11). Use the matrices

I started with:
a(1)^2 + b(1) + c = 6
a(-1)^2 +b(-1) + c = 8
a(2)^2+b*2 + c = 11

1 1 1 6
1 -1 1 8
4 2 1 11

does anyone know how to solve this further?

 

[stapel]

i have an task:
find a,b and c in the quadratic equation f(x) = ax^(2) +bx +c
which pass through the points : P(1,6), Q(-1,8) and R(2,11). Use the matrices

"Use 'the' matrices"? Did they give you particular matrices to use?

I started with:
a(1)^2 + b(1) + c = 6
a(-1)^2 +b(-1) + c = 8
a(2)^2+b*2 + c = 11

This is the correct way to start. (link to lessons)

1 1 1 6
1 -1 1 8
4 2 1 11

does anyone know how to solve this further?

Yes; reduce the matrix to row-echelon (or reduced-row-echelon) form to convert the matrix into a form from which you can determine the values of [imath]a[/imath], [imath]b[/imath], and [imath]c[/imath].

You have this matrix:

[imath]\qquad \begin{bmatrix} 1&1&1&6 \\ 1&-1&1&8 \\ 4&2&1&11 \end{bmatrix}[/imath]

One way to get started would be to add [imath]-1R_1[/imath] to [imath]R_2[/imath].

If you get stuck, please reply showing all of your steps so far. Thank you!

Eliz.

 

[khansaheb]

i have an task:
find a,b and c in the quadratic equation f(x) = ax^(2) +bx +c
which pass through the points : P(1,6), Q(-1,8) and R(2,11). Use the matrices

I started with:
a(1)^2 + b(1) + c = 6
a(-1)^2 +b(-1) + c = 8
a(2)^2+b*2 + c = 11

1 1 1 6
1 -1 1 8
4 2 1 11

does anyone know how to solve this further?

Following the advise in response #2,

Add -1*R₁ to R₂

Then

Add -4*R₁ to R₃

Please share your work.

 

[Steven G]

i have an task:
find a,b and c in the quadratic equation f(x) = ax^(2) +bx +c
which pass through the points : P(1,6), Q(-1,8) and R(2,11). Use the matrices

I started with:
a(1)^2 + b(1) + c = 6
a(-1)^2 +b(-1) + c = 8
a(2)^2+b*2 + c = 11

1 1 1 6
1 -1 1 8
4 2 1 11

does anyone know how to solve this further?

**Solve the system of three equations as you normally would.
Then go back and make two changes to the solution you obtained from **.
Change 1: Remove/erase/delete the letters (ie remove the a, b and c) from each equations you wrote in **
Change 2: Wherever you have an equal sign in ** replace it with a vertical line.