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avatar+218 

What are the coordinates of the points where the graphs of \($f(x)=x^3 + x^2 - 3x + 5$\)and \(g(x)=x^3+2x^2-8x+11\) intersect?

Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates are in increasing order. (So "(1,-3), (2,3), (5,-7)" - without the quotes - is a valid answer format.)

 Mar 7, 2024
edited by ABJelly  Mar 7, 2024
 #1
avatar+128794 
+1

Set the functions equal

 

x^3 + x^2  - 3x + 5  = x^3 + 2x^2 - 8x  + 11     simplify as

 

x^2 -5x + 6  =  0      factor as

 

(x -3) ( x -2)  = 0

 

x - 3 = 0       x  - 2   =   0

x = 3                x  = 2 

 

When x  = 2     y =  2^3 + 2^2 -3(2) + 5 =  11

 

When x =  3     y =  3^3 + 3^2 - 3(3) + 5  = 32

 

The intersection pts   are  ( 2, 11)   (3, 32)

 

cool cool cool

 Mar 7, 2024

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