I forgot how to graph these types of equations without a calculator. Can someone give me a quick rundown?
x = y - y^2
Thanks
x = y - y^2
This is the inverse function of a parabola. Consider the following equation:
$\displaystyle 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: $\displaystyle x = - (y^2 - y)$
Complete the square: $\displaystyle x = - (y^2 - y + \frac1{4} - \frac1{4})$
Take -1/4 out by multiplying it with -1: $\displaystyle x = - (y^2 - y + \frac1{4}) + \frac1{4}$
Factor the completed square: $\displaystyle x = - (y-\frac1{2})^2 + \frac1{4}$
$\displaystyle x - \frac1{4} = - (y-\frac1{2})^2$
Does this equation look familiar?
$\displaystyle y^2 - y - x = 0$
From the quadratic formula:
$\displaystyle y = \frac{1 \pm \sqrt{4x + 1}}{2}$
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
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