1. ## Graphing

I forgot how to graph these types of equations without a calculator. Can someone give me a quick rundown?

x = y - y^2

Thanks

2. also how would I graph this with my ti-89?

3. x = y - y^2

This is the inverse function of a parabola. Consider the following equation:
$x - h = \frac1{4p} (y-k)^2$

The vertex is: V(h, k)
And the need for p is to know if the function opens lefts or opens right (since this is an inverse of a parabola). Basically, if p>0, it opens right. If p<0, it opens left.

Now, first, we have to complete the square:

Rearrange the equation first:
Take -1 as common factor: $x = - (y^2 - y)$
Complete the square: $x = - (y^2 - y + \frac1{4} - \frac1{4})$
Take -1/4 out by multiplying it with -1: $x = - (y^2 - y + \frac1{4}) + \frac1{4}$
Factor the completed square: $x = - (y-\frac1{2})^2 + \frac1{4}$
$x - \frac1{4} = - (y-\frac1{2})^2$

Does this equation look familiar?

4. Originally Posted by JonathanEyoon
I forgot how to graph these types of equations without a calculator. Can someone give me a quick rundown?

x = y - y^2

Thanks
Originally Posted by JonathanEyoon
also how would I graph this with my ti-89?
$y^2 - y - x = 0$

$y = \frac{1 \pm \sqrt{4x + 1}}{2}$

As you can see this is not a function. So you have to make two graphs, one using the + sign and one using the - sign.

-Dan

5. Thanks alot guys. I appreciate it

6. Hello,

Originally Posted by JonathanEyoon
also how would I graph this with my ti-89?
You can use the graph with parameters (in MODE, choose the function mode to "parametric")

Then, y1=t and x1=t-t^2

7. wow thanks for the tip. Question. I set my 89 to parametric and input what you said but i'm only getting the top half of the graph. How do I make it so I get the both the top and bottom?

8. Originally Posted by JonathanEyoon
wow thanks for the tip. Question. I set my 89 to parametric and input what you said but i'm only getting the top half of the graph. How do I make it so I get the both the top and bottom?
Ha ! I found the problem !!!

You have to take negative values of y.

So in the window (diamond F2), configurate the t.
Here is what I've done :

tmin=-10
tmax=10
tstep=.1
xmin=-10
xmax=10
xscl=1
ymin=-10
ymax=10
yscl=1

When you graph it, you can increase the speed by increasing tstep (to .5 for example).
Then, the usual stuff, when you're in the graph window, do F2 - A to get an automatic zoom

9. Thanks alot! Very much appreciated!

10. Originally Posted by JonathanEyoon
Graph the curve with equation:
$x = y - y^2
$
Why not first sketch this graph on the y-x plane? as this sketch is very easy, then all you need to do is swap around the y and x axis to et your sketch in the x-y plane, this can be achieved easily by reflecting your graph in the line y=x.

Bobak