Finding a polynomial when only given five points

[cougarsoccer]

i just enrolled at the linear algebra class at my university. and after out first test the professor gave us this "calculator project" (meaning just using the calculator in some way to get the answer) that has 4 linear algebra application problems. i figured out the last three but i am stuck on the first one. it is in two parts.

a. determine the polynomial whose graph passes through the points (-1/2, 75/16), (0,6), (2/3, 220/81), (3,48), and (4,210)

b. the second question just says to sketch an accurate graph of the polynomial.

i went and asked the professor the other day how we might go about finding the answer. and she hinted around having a equation in the fourth degree (ax^4+bx^3+cx^2+dx+e if I'm not mistaken) all the other questions involved me making a matrix out of the system of equations and putting them in reduced row echelon form to find the answer so I'm suspecting that it must be done that way for this one too b/c that is all we have learned in the class so far. any helps or hints would be appreciated guys.

 

[rbj]

this should be moved to some homework forum.

cougar, you can set up a 5x5 system of linear equations that you can solve with any program that does that (Gaussian elimination or square matrix inversion). don't let those powers of 3 or 4 scare you; they get applied to those known x ordinates: {-1/2, 0, 2/3, 3, 4}. they're just numbers. it's the a, b, c, d, e that are your unknowns.

 

[Defennder]

This was double-posted here:
https://www.physicsforums.com/showthread.php?p=1873892