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I have a graph image that the line touches on the x-axis the values $-4, -2, 0$, and $1$.

I believe that part of the answer is $f(x) = (x+4)(x+2)(x-1)$, but what is the forth zero?

Edit: On the graph image, the line doesn't actually go through the point -4, but hovers directly above it

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"Touching the $x$-axis" occurs when $f(x) = 0$.

How can you modify your function so that $f(0) = 0$?

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    You're welcome. I suggest you do some deep thinking about why changing your function as above gave the desired graph; I won't say anything more about it here, but be sure to ask your teacher/instructor if you are still unclear on the matter.2012-10-30
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Answer would be $f(x) = x(x-1)(x+2)(x+4) $. This will give you all the zeros you are looking for. Trick is to make sure your function is zero at each of the values 0,1,-2, and -4.

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    this probably would be the right answer if that was the question that my homework was telling me :)2012-10-30