The graphs of y = 3 - x + x^3 and y = 1 + x + x^2 + x^3 The graphs of and intersect in multiple points. Find the maximum difference between the y-coordinates of these intersection points.

Guest Feb 22, 2021

#1**0 **

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

1 + x + x^2 = 3 - x

x^2 + 2x - 2 = 0

So, we can use the quadratic equation to find the 2 ys, or we can simpify it a bit first.

(-b+sqrt(b^2-4ac))/2a- (-b-sqrt(b^2-4ac))/2a = sqrt(b^2-4ac)/a

Now, the difference is sqrt(b^2 - 4ac).

sqrt(2^2 - 4(-2))/1

sqrt(8)

2sqrt(2)

I hope this helped. :))

=^._.^=

catmg Feb 22, 2021

#2**+1 **

Equate the two polynomials and solve for the x points of intersection

3-x = 1+x+x^2

x^2 +2x -2 = 0

Well it said 'graphing' in the Q ....so here is the graph of the two polynomials

I think you can take it from here !

ElectricPavlov Feb 22, 2021