Question

How would you turn this into Vertex Form: y=x^2 -2x -5?

Answer 1

Do you know how to complete the square?

Answer 2

Yes.

Answer 3

That's what you do

Answer 4

Oh ok. But what would you factor out from the equation?

Answer 5

I would take 1/2 the coeff in front of x, square it. add and subtract it (this is like adding zero):

y= x^2 -2x +1 -1 -5
or
y= (x^2-2x+1) -6

the stuff in parens is (x-1)^2 (completed the square)
y= (x-1)^2 -6
that is vertex form

Answer 6

I partly get it now, where did you get the -5 from?

Answer 7

y=x^2 -2x -5
y +5 = x^2 - 2x
y +5 + 1 = x^2 - 2x + 1
y + 6 = (x-1)^2
y = (x-1)^2 - 6

Answer 8

Oh ok. I get it now, it makes since now. Thanks.

Answer 9

I'm glad you understood it.

Answer 10

I'm not a big fan of skipping steps, and unfortunately, the way phi did it is indeed the way it is taught in school and I doubt if people even understand that steps are skipped when calculating it that way.

With my way, you don't skip steps. You simply do all of the proper operations from beginning to end, step by step.

Answer 11

I did not skip any steps. Look carefully

Answer 12

Yeah, that's like me. If I skip steps, I mess up; so I have to do every step in order. My teacher also skips steps, and it annoys me.

Answer 13

phi, you skipped steps, lol. The fact that you don't realize you skipped steps is what makes it worse. You didn't skip steps according to the way it was taught to you, but that doesn't mean you didn't skip steps.

Answer 14

@phi , the first proper step is to add 5 to both sides...

Answer 15

My teacher teaches like Phi, he gets the right answer, but he skips steps to get to it.

Answer 16

The thing is, the way Phi and your teacher teaches it is the way it is taught in school. They don't realize they are skipping steps when they do it. It is a standard procedure but it does indeed skip steps, which leads to confusion.

Answer 17

My teacher realizes he skips steps, on purpose. To see if we are paying attention. But I get confused. Which makes it harder to understand the problem. I like the way you showed it, Hero, you don't skip steps and it's like you are walking me through it.

Answer 18

@Hero, you are following a formula which is fine, but all we have to do is add zero to the equation:
y= x^2 -2x -5
y= x^2 -2x +1 -1 -5 (note that +1 -1 = 0)

group terms, to get y= (x-1)^2 -6
It is not necessary to move the -5 to the left-hand side, except to help you not get confused.

Answer 19

It's good that you put it that way. I wasn't following any formula by the way...
That is just a procedure that I made up to help students like @theapplefreak understand it.

Answer 20

If you want students to understand your steps @phi , it is important that you mention things like adding zero to the equation. That step is probably what had @theapplefreak confused all along.

Answer 21

The way you did that just now, Phi, made it look like you just made the -6 come out of nowhere. You had y=x^2 -2x +1 -1 -5 (1-1=0); y=x^2 -2x -5. But where the -6 come from, @Phi?

Answer 22

He added the equivalent of zero to the equation. It's the one number that you can add to one side of an equation without having to add it to both sides.

Answer 23

What he did is prove that he didn't skip any steps, which now I agree with him, but nevertheless, choose whichever method you are comfortable with.

Answer 24

Yes, but 0-5 is -5 not -6.
I am comfortable with your method, @Hero, no offense to @phi, Hero's is just easier to understand.