Sketching these curves is a form of madness! How can I make sense of them?

[zeion]

Homework Statement

I need to sketch these curves and find where they intersect:

x+y-y^3 = 0
x-y+y^2=0

Homework Equations

The Attempt at a Solution

I have no idea what these are supposed to look like.. other than that x = -y^2+y is a sort of parabola that opens to the right.

Any tips as to how to understand functions in these forms?

 

[willem2]

These are easy, because you can get them in the form x=f(y). Just compute x for different values of y.

 

[zeion]

Any general rule about how these look like without plotting the points?
(Like for the thing with y^3?)

 

[Mark44]

The first equation can be written as x = y³ - y, and the second as x = y² - y. At a point of intersection point, the x-value on one curve has to equal the x-value on the other curve, and the same is true for the y-values.

Setting the two expressions for x equal gives us
y³ - y = y² - y
This is simple to solve, and you don't need to plot any points to do it.

 

[Char. Limit]

He says he needs to sketch the curve as well, though.

Quit thinking that the y-axis must be dependent. Pick some y points and find where the x values are at those points. You'll figure out the shape.