Question

Algebra 2! Help, equasion pictured below.

Answer 1

I'm here

Answer 2

Sorry, I was helping someone else,

Answer 3

@alyssajobug you there still?

Answer 4

yes

Answer 5

@doulikepiecauseidont

Answer 6

Ok basically, and pay attention to this cause this'll help you a lot later.

When you have a parent function, whether it be

\[\Large y=x ~\]
\[\Large y=x^2\]
\[\Large y=|x|\]
\[\Large y=\sqrt{x}\]

Answer 7

@pgpilot326 Yeah, I was just gonna show her horizontal shifts and then expand it

Answer 8

Anyways back to the question, you have those parent functions and they call them parent functions because that's the "original function" how you would say it (its the function with nothing added to it as you'll see in a second)

Answer 9

We'll work with the \[\Huge y=x^2\] since that's what we're given

Basically the fully form of this equation is \[\Huge y=a(x-h)^2+k\]

Answer 10

I know might look confusing but this is basically just
a=a stretch factor (how much the graph opens out or up
(h,k)=the vertex (the highest or in this case of y=x^2) the lowest point of the graph

Answer 11

You should also note that h is a point you must subtract so if you have the vertex at (2,3)
it would be (x-2)^2+3 and if it was (-2,3) then you'd have (x-(-2))^2+3=(x+2)^2+3

Answer 12

Now for the parent function the equation really looks like \[\Huge y=1(x-0)^2+0=~~y=x^2\]

Answer 13

Which goes back to the "parent" and original thing I was talking about.

Now anyways enough of my talking

Since this only seems to have moved horizontally, we'll only be working with h, a still=1, and k is still 0 since the graph doesn;t move up or down

Answer 14

following @alyssajobug ?

Answer 15

ya, i think so

Answer 16

@doulikepiecauseidont

Answer 17

Ok now when you move to the left or right its called a horizontal shift and when you move up and down its called a vertical shift

Answer 18

Move to the left it's \[\Large (x+h)^2\]

Answer 19

When you move to the right by h units its \[\Large (x-h)^2\]

Answer 20

Plugging into the equation that we're moving to the left and its 5 spaces we get \[\Large y=1(x+5)^2+0\] since we didn't go up or down and the graph didn't stretch or compress when looking at the graph and now you have to do is simplify this yo got it @alyssajobug

Answer 21

So I got the y=x²+25+0 from there to finish it, but that isnt an option for my question... did I miss something there?

Answer 22

Yes, do you know how to do binomial expansion?

Answer 23

no, the instructions for this lesson was a joke

Answer 24

Ok well basically go here http://www.mathsisfun.com/algebra/polynomials-multiplying.html

Answer 25

I could teach it here but I'd do no justic compared to this website becuase it covers everything you'll need and Ik it wont make sense now but this up there is just \[\Huge y=(x=5)^2=(x+5)(x+5)\]

Answer 26

alright, I'll look through it and let you know if I have anymore questions!

Answer 27

Alright and multiply that out up there and you'll have your answer

Answer 28

Actually, it would be nice to get the basics before reading those instructions there, can you do that then?

Answer 29

The basics? What do you mean?

Answer 30

That really was going through the basics, like what a polynomial is and how to multiply them together cause that would take a lot of typing and examples and writing and thats why the page is so long lol and it has a lot of them for easy learning.