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 September 22nd, 2011, 04:26 PM #1 Newbie   Joined: Sep 2011 Posts: 18 Thanks: 0 Finding a polynomial function given a graph So I really have no idea how to do this whatsoever. I've been given a graph of a polynomial function of at least degree 4 (it can be intersected by a horizontal line four times). It has three zeros going through the x axis at 0 and 4 and touching from above it at -2. One other point, at (-1, 5) was also given. I have to find a function to describe this graph and I dont't even know where to begin. Any help would be appreciated.
 September 22nd, 2011, 04:39 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs Re: Finding a polynomial function given a graph With zeroes at (0,0), (4,0) and (-2,0) (this one tangent so it must be a root of multiplicity 2 for a total of 4 roots) means we may write: $f(x)=kx(x-4)(x+2)^2$ We are given $f(-1)=5$ thus: $k(-1)(-1-4)(-1+2)^2=5$ $5k=5$ $k=1$ giving: $f(x)=x(x-4)(x+2)^2=x^4-12x^2-16x$
 September 22nd, 2011, 04:49 PM #3 Newbie   Joined: Sep 2011 Posts: 18 Thanks: 0 Re: Finding a polynomial function given a graph Thanks so much!!

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