1. ## Completing the Square

I have no idea if this is the right place to post this, but here goes:

x^2 - 4x + 8y + 4 = 0

If someone could please detail each individual step, that would be awesome.

2. Originally Posted by saintv
I have no idea if this is the right place to post this, but here goes:

x^2 - 4x + 8y + 4 = 0

If someone could please detail each individual step, that would be awesome.

You don't have to complete the square if you move things around:

$\displaystyle x^2-4x+8y+4=0$

And let's switch the places of the $\displaystyle 8y$ and the $\displaystyle 4$

$\displaystyle x^2-4x+4+8y=0$

Now let's factor

$\displaystyle (x-2)(x-2)+8y=0$

$\displaystyle (x-2)^2+8y=0$

3. Originally Posted by artvandalay11
You don't have to complete the square if you move things around:

$\displaystyle x^2-4x+8y+4=0$

And let's switch the places of the $\displaystyle 8y$ and the $\displaystyle 4$

$\displaystyle x^2-4x+4+8y=0$

Now let's factor

$\displaystyle (x-2)(x-2)+8y=0$

$\displaystyle (x-2)^2+8y=0$
Thank you! Now, how would that be written in the (y-k) = a(x-h)^2 form?

4. Originally Posted by saintv
Thank you! Now, how would that be written in the (y-k) = a(x-h)^2 form?

Well we have $\displaystyle (x-2)^2+8y=0$

And you want the x on the other side so lets subtract $\displaystyle (x-2)^2$ from both sides

$\displaystyle (x-2)^2+8y-(x-2)^2=-(x-2)^2$

$\displaystyle 8y=-(x-2)^2$

And divide by 8 to get

$\displaystyle y=-\frac{1}{8}(x-2)^2$

In this case $\displaystyle k=0$

5. Thank you! :d