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What are the coordinates of the points where the graphs of f(x) = x^3 - x^2 + x + 1 and g(x) = x^3 + x^2 + x + 1 intersect? Give your answer as a list of points separated by semicolons, with the points ordered such that their x-coordinates are in increasing order. (So "(1,-3); (2,3); (5,-7)" - without the quotes - is a valid answer format.)

 Jun 25, 2022
 #1
avatar+16 
+2

Desmos says it's only (0,1)

 Jun 25, 2022
 #2
avatar+124676 
+1

Set the euations   equal

 

x^3 - x^2 + x + 1 =  x^3 + x^2 + x + 1    rearrage as

 

2x^2  =  0                    divide through by  2

 

x^2   = 0

 

x = 0

 

And using either equation  y  = (0)^3 + (0)^2  + 0 + 1     =   1

 

So......the intersection point  is (0,1)

 

 

 

 

 

 

cool cool cool

 Jun 25, 2022

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