1. Feb 4, 2010

### zeion

1. The problem statement, all variables and given/known data

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

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

2. Relevant equations

3. 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?

2. Feb 4, 2010

### willem2

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

3. Feb 4, 2010

### zeion

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

4. Feb 5, 2010

### Staff: Mentor

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.

5. Feb 5, 2010

### Char. Limit

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

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