1. ## transformation x^2+2x

What effect does adding or subtracting x have to a graph, for example in the graph x^2+x? What if you changed it to x^2+2x, or some other co efficient, what is the transformation exactly?

I don't think this falls into my curriculum so I can't find it in my text book, so I was just wondering !

2. Originally Posted by shawli
What effect does adding or subtracting x have to a graph, for example in the graph x^2+x? What if you changed it to x^2+2x, or some other co efficient, what is the transformation exactly?

I don't think this falls into my curriculum so I can't find it in my text book, so I was just wondering !
I'll do the easy one ...

$y = x^2+2x$

$y = x^2 + 2x + 1 - 1$

$y = (x+1)^2 - 1$

$y = (x+1)^2 -1$ is the graph of $y = x^2$ shifted left one unit and down one unit.

3. thank you

did that only work out because it happened to be a square pattern?
what is the transformation otherwise ?

4. Originally Posted by shawli
thank you

did that only work out because it happened to be a square pattern?
what is the transformation otherwise ?
it worked out because I made it a "square" pattern ... the method used is called completing the square.

it can be used for other values of linear coefficients, but is easiest if the linear coefficient value is an even number.

5. Originally Posted by skeeter
I'll do the easy one ...

$y = x^2+2x$

$y = x^2 + 2x + 1 - 1$

$y = (x-1)^2 - 1$

Shouldn't this be (x+1)^2-1 ??

$y = (x-1)^2 -1$ is the graph of $y = x^2$ shifted right one unit and down one unit.