Question
Find the points of intersection of the graphs of the equations.
x = 3 − y^2
y = x − 1
x = 3 − y^2
y = x − 1
Answers
Reiny
from the 2nd :
y = x − 1
x = y+1
sub that into the first:
y+1 = 3-y^2
y^2 + y - 2 = 0
(y+2)(y-1) = 0
so y = -2 or y = 1
if y = -2, x = -2+1 = -1, so they intersect at (-1,-2)
if y = 1, x = 1+1 = 2, and they intersect at (2,1)
verification:
y = x − 1
x = y+1
sub that into the first:
y+1 = 3-y^2
y^2 + y - 2 = 0
(y+2)(y-1) = 0
so y = -2 or y = 1
if y = -2, x = -2+1 = -1, so they intersect at (-1,-2)
if y = 1, x = 1+1 = 2, and they intersect at (2,1)
verification:
Reiny
verification:
http://www.wolframalpha.com/input/?i=plot+x+%3D+3+%E2%88%92+y%5E2+,+y+%3D+x+%E2%88%92+1
http://www.wolframalpha.com/input/?i=plot+x+%3D+3+%E2%88%92+y%5E2+,+y+%3D+x+%E2%88%92+1
Anonymous
Thank you I understand now