Please Help!! Im Soooo Lost!!

Your friend runs up to you, scared that he is not ready for the upcoming quadratics test. To help him study, you will create four different quadratic functions. Then demonstrate to him how to rewrite each function as a group of factors, if possible.
The function f(x) is a difference of squares.
The function g(x) is a sum of squares.
The function h(x) is a perfect square trinomial.
The function j(x) can only have a GCF factored out of it

Question

Please Help!! Im Soooo Lost!!

Your friend runs up to you, scared that he is not ready for the upcoming quadratics test. To help him study, you will create four different quadratic functions. Then demonstrate to him how to rewrite each function as a group of factors, if possible.
The function f(x) is a difference of squares.
The function g(x) is a sum of squares.
The function h(x) is a perfect square trinomial.
The function j(x) can only have a GCF factored out of it

imstuck · Answer

You have to do all 4 of those?

imstuck · Answer

OS is messed up; you will keep getting those diamond shapes.  It's not your computer.

anonymous · Answer

Yep and thats only question number 1, and thanks

imstuck · Answer

What exactly do you have to do with them?  Make an example and then graph it or something? I'm kinda confused on what you have to do with them.

imstuck · Answer

A difference of squares function could be this, for example:  f(x) = (x+3)(x-3)

anonymous · Answer

Im not asking for the answer just how to do it. According to the question i have to rewrite each function as a group of factors, if possible.

imstuck · Answer

The actual function is$$f(x) = x ^{2}-9$$

imstuck · Answer

I guess writing that in a group of factors would be the (x-3)(x+3), right?

anonymous · Answer

Okay and how did you get that??

anonymous · Answer

and yes

imstuck · Answer

As a function, the differece between 2 squares is found by taking x andd squaring it to get x^2, then any number squared would be the number.  3 squared is 9, so x^2 - 9 is the difference bewteeen two squares.  You could have said x^2-16 or x^2-25, as long as the x is squared and the number after it is a perfect square.  Got that?

anonymous · Answer

Yepp thanks :D

anonymous · Answer

Now what about the sum of squares

imstuck · Answer

The number after the x^2 HAS to be a perfect square.  Like 10 would not work, cuz 10 is not a perfect square.

imstuck · Answer

Do you have to do anything else with each one?  Like graph them or anything?

anonymous · Answer

Not until question number 4

imstuck · Answer

Ok, for the sum of 2 squares, you could write something like this:$$f(x)=x ^{2}+4$$because that is the sum of 2 perfect squares, but they cannot be written in factored form.  Only the difference of perfect squares can be written in perfect binomials.  In other words, x^2 + 4 cannot be factored.  If you tried to write it as (x+2)(x+2) you would get x^2 + 4x + 4, which is very definitely not the same as x^2 + 4.

imstuck · Answer

BTW the graph for the first one looks like this:|dw:1411600887513:dw|and the graph for the second one looks like this:|dw:1411600932396:dw|