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How to you get the equation of a cubic from its graph?

For example:

If this is a graph of ax^3+bx^2+cx+d, what is a+b+c+d?

 Jul 21, 2019
edited by Davis  Jul 21, 2019
 #1
avatar+6034 
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\(\text{you can see the zero crossings are at $x=0, x=1, x=2$}\\ \text{Thus the curve is given by }\\ f(x) = x(x-1)(x-2) = x^3-3 x^2+2 x\\ a+b+c+d =1-3+2= 0\)

 

 

\(\text{one can be a bit more clever and note that in general}\\ a+b+c+d = f(1)\\ \text{and we know that $1$ is one of the zeros so}\\ a+b+c+d=f(1)=0\)

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 Jul 22, 2019
edited by Rom  Jul 22, 2019
 #2
avatar+507 
+1

thanks!

Davis  Jul 27, 2019

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