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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 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.)

 Oct 9, 2024
 #1
avatar+37146 
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Where the graphs intersect, they are equal :

x^3 + x^2 -3x + 5   =  x^3 + 2x^2

x^2 -3x + 5 = 2x^2 

0 =  x^2 +3x -5

   Now use Quadratic Formula with   a = 1  b = 3  and c = -5    to find x = 1.193    and -4.193

   Now use these values of 'x' in either of the equations to find the corresponding 'y' coordinates.  

 Oct 10, 2024

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