What is the point of intersection for y=2x^2-8x-1 and y=x^2+3x+9?

1 Answer
May 8, 2018

Points of intersection are #(11.85,184.84)# and #(-0.85,7.18)#

Explanation:

One can get the pint of intersection by solving these simultaneous equations. As #y=2x^2-8x-1# and #y=x^2+3x+9#, we have

#2x^2-8x-1=x^2+3x+9#

or #x^2-11x-10=0#

or #x=(11+-sqrt(121+40))/2#

i.e. #x=(11+-sqrt161)/2=(11+-12.69)/2#

i.e. #x=23.69/2=11.85# or #-1.69/2=-0.85#

and then if #x=11.85#, #y=184.84# and if #x=-0.85#, #y=7.18#

and points of intersection are #(11.85,184.84)# and #(-0.85,7.18)#

graph{(y-2x^2+8x+1)(y-x^2-3x-9)=0 [-20, 20, -87.5, 232.5]}