Question

Please help!
Described how the graph of y = (2x+2)^2 can be obtained from the graph of y = x^2.

Answer 1

http://www.wolframalpha.com/input/?i=Plot+%282x%2B2%29^2%2C+x^2

Answer 2

But how can graph 1 be obtained from graph 2?
I'm not sure how this helps me. What do I do with this?

Answer 3

Make different plots until u see the pattern, that way you will learn it better.

For example

http://www.wolframalpha.com/input/?i=Plot+%28x-1%29%5E2%2C+%28x%2B1%29%5E2%2C+x%5E2+for+x+in+-5..5

Answer 4

The pattern I see is that when x is squared, it is a parabola. Is there another pattern I should be looking for?

Answer 5

y = (2x+2)^2

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

y = 2^2*(x+1)^2

y = 4(x+1)^2

Compare this with y = a(x-h)^2 + k

Answer 6

All of those equations are the same parabola, right?

Answer 7

they are

Answer 8

I'm not sure what I'm supposed to do with that.

Answer 9

Say for example you go from y = x^2 to y = (x-1)^2

You're shifting it 1 unit to the right

Answer 10

if you can get it into the form y = a(x-h)^2 + k, you can determine how to shift and how to stretch/compress it

Answer 11

But adding k would be determining where on the y-axis the vertex would be. So why would I want to change the y-axis vertex?

Answer 12

you can easily make k = 0 to make sure it doesn't shift up/down

Answer 13

Oh! I think I get it now!

Answer 14

Kinda...
So basically the answer to this question would be explaining how to evolve y = (2x+2)^2 into the y = a(x-h)^2 + k format. Am I anywhere close to what you've been trying to explain?

Answer 15

yes you are

you turn y = (2x+2)^2 into y = 4(x+1)^2

which is in y = a(x-h)^2 + k form where a = 4, h = -1 and k = 0

Answer 16

since h = -1 , you shift y = x^2 1 unit to the left

you don't shift up or down because k = 0

Answer 17

a = 4 means that you stretch everything vertically by a factor of 4

Answer 18

Thank you. I think I have a better understanding of this material. Now I just have to put it into words on the page. :P

Answer 19

yw