SOLUTION: Given the graph of a polynomial, how do I find the equation of its function? I wish I could show you the graph... Ok, I have figured out how to estimate the degree of a funct

Question 72891: Given the graph of a polynomial, how do I find the equation of its
function? I wish I could show you the graph...
Ok, I have figured out how to estimate the degree of a function by
looking at its graph. For example, the MAXIMUM number of turning
points a sixth-degree polynomial can have is five, but that it can
have less as well. I have a graph that I have determined to most
likely be that of a sixth-degree polynomial. It has 3 turning
points, and 6 zeroes. However, I also understand that the graphs of
sixth-degree polynomials can have various 'appearances'. That is
why I don't understand how I can possibly give the equation for a
function, given its graph. Help!

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You can look at the roots and accurately guess the equation. If the roots are x=2, x=3 and x=5, then your equation will be (x-2)(x-3)(x-5) which will turn into a long and nasty polynomial of degree 3 (which I don't want to write out). So look at the roots and know the fact that if the root is x=a then the factor is (x-a). However, this does not help all the time (it will in your case) since not all of the zeros will be real, but that's for another day.
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