(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using a simple "trick," you can find a polynomial function whose graphi goes through any given set of points. For example, the graph of the following function goes through the points (1, 3), (2, 5), and (3, -1).

[tex]f(x) = 3\;\frac{(x-2)(x-3)}{(1-2)(1-3)} \;+\; 5\frac{(x-1)(x-3)}{(2-1)(2-3)} \;+\;(-1) \frac{(x-1)(x-2)}{(3-1)(3-2)}[/tex]

Find a polynomial function g that satisfies g(-2) = 1, g(0) = 3, g(1) = -2 and g(4) = 3

2. Relevant equations

(Above)

3. The attempt at a solution

[tex]g(x) = (1)\frac{(x-1)(x-4)}{(-2-1)(-2-4)} \; + \;(-2)\frac{(x+2)(x-4)}{(1+2)(1-4)} \;+ \;3\frac{(x+2)(x-1)}{(4+1)(4-1)}[/tex]

I cannot figure out how to produce g(0) = 3.

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# Homework Help: Fitting a Function given 3 points

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