The graphs of $y=x^2$ and $x+y=0$ intersect at two points. Find the distance between these two points.

x + y = 0

y = -x

Sub this into the first equation

-x = x^2

x^2 + x = 0

x ( x + 1) = 0

Set both factors to 0 and solve for x

x = 0 and x = -1

When x = 0 y = 0

When x = -1 , y = 1

(0,0) and (-1, 1)

Distance between these = sqrt [ (-1)^2 + 1^2 ] = sqrt (2)