# v-shaped vertices

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I don't understand equations like this: y = |x + 2| I know you subtract 2 so you can get rid of the posotive 2 but why do you do that and where does the 2 go? When you graph this I know you move the vertix two places to the left but why? I really don't undeerstand these at all.

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Quote:
 Original post by subfloodI don't understand equations like this: y = |x + 2|I know you subtract 2 so you can get rid of the posotive 2 but why do you do that and where does the 2 go? When you graph this I know you move the vertix two places to the left but why? I really don't undeerstand these at all.

i really dont understand you at all either.

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y = |x + 2|

I don't know why when you graph this you move to the left 2 spaces.

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I guess he's talking about graphs of functions.

y = x, makes a diagonal line right?

y = |x| makes a v-shape, reflecting at the y axis.
e.g.
|2| = 2.
|-2| also = 2.

y = x + 2 makes a diagonal line offset by 2

So y = |x + 2| makes a V-shape, offset by 2.

Hope this helps
Pete

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"So y = |x + 2| makes a V-shape, offset by 2."

but shouldn't the point on the line be (2, 0) instead of (-2, 0)?

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Quote:
 Original post by subflood"So y = |x + 2| makes a V-shape, offset by 2."but shouldn't the point on the line be (2, 0) instead of (-2, 0)?

no.

just fill in the values and youll see its right.

|x+2| = 0 -> x = -2

im sorry but i think this is a (bluntly put) stupid question. this forum is supposed to be about math as it relates to gamedev, if there is anything this relates to its elementary school.

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why |x + 2| = 0? why not |x + 2| = 5

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Quote:
 Original post by subfloodwhy |x + 2| = 0? why not |x + 2| = 5

sigh.

were looking for a point on the x-axis, ie y = 0

y = |x + 2| = 0

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To subflood:
You can see the problem more clearly if you decomposed it into two equations

y = x + 2 for all x+2 >= 0 -> x >= -2

and

y = - (x + 2) for all –(x + 2) >= 0 -> x <= -2

so you are correct the equation is a V shape line centerd at the point (-2, 0)

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Quote:
 Original post by Eelcoim sorry but i think this is a (bluntly put) stupid question.

I don't think it's a stupid question, I just think it's being asked in a stupid way. It is a little counter-intuitive,
given the graph of y = |x|:

y = |x| + 2 shifts it UP 2 units, while
y = |x + 2| shifts it LEFT 2 units.

Why is that? I think is what he's asking. Without looking at the graphs or really thinking about it, you might guess that if y = |x|+2 shifted it up, then y = |x+2| should shift it right. The same principle applies to graphing ellipses, hyperbola, or any graph, so it is important. Just like while |x|*2 makes it stretch upward, |x*2| makes it compress sideways.

You can think of it like (still using y = |x| as the baseline), now think about x = 0. you have y = |0|. Now for x + 2 to produce that same result, it has to be 2 Fewer, so you get |(-2) + 2| = |0|. So for that same value of y, x is 2 fewer than in the y = |x| graph.

It makes sense when you think "x + 2 doesn't actually add 2 to the x you're graphing, rather it subtracts 2 from the value that x has to be to produce the same result as if x were alone" strange but true.

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