# Thread: Vertex form and perfect squares

1. ## Vertex form and perfect squares

Hey guys, I was wondering if someone can help me through a step by step guide on writing in vertex form.

I have this equation: -2x^2+6x+1
On this equation I factored out the 2 leaving me with: 2(x^2+3x)+1
Then I did (3/2)^2 and came out with 9/4.
At this point the book lost me, I can't seem to find out what to do next after finding that.

On perfect squares I don't even know how to find the value of k.
I have this equation: x^2-kx+100=0
I think I would have to subtract 100 from both sides, but I'm not sure.

2. Originally Posted by Jubbly
Hey guys, I was wondering if someone can help me through a step by step guide on writing in vertex form.

I have this equation: -2x^2+6x+1
On this equation I factored out the 2 leaving me with: 2(x^2+3x)+1
Then I did (3/2)^2 and came out with 9/4.
At this point the book lost me, I can't seem to find out what to do next after finding that.

On perfect squares I don't even know how to find the value of k.
I have this equation: x^2-kx+100=0
I think I would have to subtract 100 from both sides, but I'm not sure.

$\displaystyle -2x^2+6x+1$

$\displaystyle -2(x^2-3x) + 1$

$\displaystyle -2\left(x^2 - 3x + \frac{9}{4}\right) + 1 + \frac{9}{2}$

$\displaystyle -2\left(x - \frac{3}{2}\right)^2 + \frac{11}{2}$

x^2 - kx + 100

you know it has to factor to $\displaystyle (x-10)^2$ ... what would be the middle term if you expanded $\displaystyle (x-10)^2$ ?

3. Actually when you take out the common factor of $\displaystyle 2$ it needs to come from every term.

So $\displaystyle \displaystyle -2x^2 + 6x + 1 = -2\left(x^2 - 3x - \frac{1}{2}\right)$

$\displaystyle \displaystyle = -2\left[x^2 - 3x + \left(-\frac{3}{2}\right)^2 - \left(-\frac{3}{2}\right)^2 - \frac{1}{2}\right]$

$\displaystyle \displaystyle = -2\left[\left(x - \frac{3}{2}\right)^2 - \frac{9}{4} - \frac{2}{4}\right]$

$\displaystyle \displaystyle = -2\left[\left(x - \frac{3}{2}\right)^2 - \frac{11}{4}\right]$

$\displaystyle \displaystyle = -2\left(x + \frac{3}{2}\right)^2 + \frac{11}{2}$.

4. The "2" doesn't have to come from every turn because you take the last term out anyway. What skeeter did was perfectly valid.

5. Originally Posted by HallsofIvy
The "2" doesn't have to come from every turn because you take the last term out anyway. What skeeter did was perfectly valid.
Skeeter wrote his post at the same time as mine. You are right, there's nothing wrong with Skeeter's method. However, what I wrote is the standard method.