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.
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
I hope this helped. :))