Question

Use a graphing calculator to write a polynomial function to model this set of data

{(5,2) (7,5) (8,6) (10,4) (11, -1) (12 -3) (15,5) (16,9)}

A) f(x) = 2x3 + 2.70x2 + 0.09x - 65.21

B) f(x) = 2x3 - 0.09x - 65.21

C) f(x) = 0.09x3 - 2.70x2 + 24.63x - 65.21

D) f(x) = x4 - 5.7x3 + 2.70x2 + 24.63x - 65.21

Answer 1

It is a bit difficult to show you such a graph here.

What you want to do is graph those functions in the domain from about (0,-10) to (20,10) and put your discrete points on the graph. Then you can see which function comes close to the points.

for example your first function looks like this
http://www.wolframalpha.com/input/?i=2x3+%2B+2.70x2+%2B+0.09x+-+65.21+%2C+x%3D-10+to+%2B10

it seems for example you do not want 2 x^3 in there because it is huge for x = 15 for example. so A and B are questionable and D does not look so hot either.