What are the intercepting points of

Question

y^2=-4x and x^2=y

I set both equations equal to 0, but only get x=0 and there is another intercepting point. please help!

Graphically, y=x^2 is positive for all values of x, whether positive or negative.
The second equation is y positive for the
negative values of X without getting into imaginary numbers. The curves intersect at y=~2.5 and x=~1.6

Analytically, solve y^2=-4X for x, then substitue in Y=x^2. After factoring, you get a cubic equation y^3-16=0. Only one root isn't imaginary: y=2.52 When you substitute that to solve for x, it is -1.59, which checks with the graph.