SOLUTION: Use a system of equations to find the cubic function f(x) = ax^3 + bx^2 + cx + d that satisfies the equations. Solve the system using matrices. f(−1) = 6 f(1) = 4 f(2)

Question 1120020: Use a system of equations to find the cubic function
f(x) = ax^3 + bx^2 + cx + d that satisfies the equations. Solve the system using matrices.
f(−1) = 6
f(1) = 4
f(2) = 15
f(3) = 42
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Good idea.
Do you know how to do that?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

if

and

then

Which is to say

Similarly,

and finally,

Then your augmented matrix is:

Just use Gauss-Jordan row-reduction to calculate your coefficients. Alternatively, you can calculate the five determinants and use Cramer's Rule. Easy-peasy if you use the MDETERM function in Excel.

John

My calculator said it, I believe it, that settles it

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SOLUTION: Use a system of equations to find the cubic function f(x) = ax^3 + bx^2 + cx + d that satisfies the equations. Solve the system using matrices. f(&#8722;1) = 6 f(1) = 4 f(2)

SOLUTION: Use a system of equations to find the cubic function f(x) = ax^3 + bx^2 + cx + d that satisfies the equations. Solve the system using matrices. f(−1) = 6 f(1) = 4 f(2)