Help 5 worded math questions I don't understand

Question

anonymous · Answer

attachment

anonymous · Answer

@mathslover can you help me threw this

anonymous · Answer

@divu.mkr ? any chance you can help me/?

anonymous · Answer

@e.mccormick can you help me?

e.mccormick · Answer

The easy way to do the first one is to write the result, say a difference of squares, and then multiply it.  Then you know the resulting function will factor to a difference of squares, etc.

anonymous · Answer

can you show me?

e.mccormick · Answer

Well, look at the first part of 1. Know what a difference of squares is?

anonymous · Answer

yes its like this right f(x)=9x^2-25 thants my answer for f(x)?

anonymous · Answer

and sum of squares would be the opposite sign posotive g(x)=9x^2+25 right?

e.mccormick · Answer

Yes.  So those two are easy.  Perfect square trinomial?

anonymous · Answer

not sure about that one can you give me an example?

e.mccormick · Answer

$(ax+b)^2$  so put in any numbers for a and b, then multiply it.

e.mccormick · Answer

As long as the answer comes out to a trinomial, so 3 parts, it is a winner.

e.mccormick · Answer

$(2x+4)(2x+4) \implies $
$4x^2+8x+8x+16 \implies $
$4x^2+16x+16  $

So there it is.

anonymous · Answer

ohh k what about The function j(x) can only have a GCF factored out of it.

e.mccormick · Answer

Same thing.  Find something that would be a GCF, put it next to a binomial, multiply.

anonymous · Answer

can you show me an example

e.mccormick · Answer

Well, do you know a binomial that can't be factored?

anonymous · Answer

no not sure

e.mccormick · Answer

Well, any variable without a power can't be factored.  So if there is only an x, no powers, then whatever else is there just sits there.

anonymous · Answer

6a3b4 + 9a6b3 ? would this be one?

e.mccormick · Answer

Hmmm...
$6a^3b^4 + 9a^6b^3$ ?

anonymous · Answer

yes lol

e.mccormick · Answer

$6a^3b^4 + 9a^6b^3$
$3(2a^3b^4 + 3a^6b^3)$
$3a^3b^3(2b + 3a^3)$

That should do.

My point was $x(x+5)=x^2+5x$ which also qualifies.  =)

anonymous · Answer

ohh okay thanks can you help me with #2 thats the one that kinda confuses me

e.mccormick · Answer

Know your shifts and other changes to graphs?

anonymous · Answer

no

e.mccormick · Answer

OK. The topic is called transformations. Here is a page just on that: http://www.purplemath.com/modules/fcntrans.htm Lot quicker than trying to type it all. =)

anonymous · Answer

okay i guess i understadn a little bit

e.mccormick · Answer

Here, try this one... it is harder to find things on this site, but I think they do a really good job of showing it: http://www.regentsprep.org/regents/math/algtrig/ATP9/funclesson1.htm

e.mccormick · Answer

The key concepts are the thumbtack part, like "Slide to the right or left" which is what you are looking for.  Then, what it means and an explanation are right there.

anonymous · Answer

thanks for the help but i don't understand it at all. :/ really i appreciate it just i don't understand it sorry. bye

e.mccormick · Answer

Well, it says $k(x)=x^2$, then the first one is k(x+c).  That means:

$(x+c)^2$

If you go to that page it says:
Slide to the right or left
$f (x + a) $translates $f (x)$ horizontally

There it is.  The answer to that one part.  Next to it is an explanation of why.