Find the coordinates of the intersections :)

Question

Find the coordinates of the intersections of 

 

y1=x-(x^3/6)+(x^5/120)

 

y2=x^2

 

 

Make a sketch of the functions on the grid below. Estimate the x,y coordinates to decimal places. There are 3 intersections. The third intersection will be out of range of the grid provided, so just show the first 2 intersections but be sure to state all three intersections in your final answer.

 

PHOTO: https://hishsaka.smugmug.com/Math/i-L4CqCq7/A

Answer 1

x - x^3/6 +x^5/120 = x^2

x^5/120 -x^3/6 -x^2 + x = 0

x/120[x^4 -20x^2 -120x + 120] = 0

set the factors = 0, solve for x

one point of intersection is the origin (0,0)

there are potentially 4 more. but 2 are imaginary.

the other two x intersections are about (1,0) and (6,0)

but closer to (.8, 0) and (6.05, 0)