Question

I really need some help getting started on this quiz.
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.

Answer 1

The function f(x) is a difference of squares.
you will want x^2 and a perfect square. (example 9 or 25)

Answer 2

I'm sorry, I don't understand what it means saying "difference of squares"
or maybe I am over thinking the wording and it just means \[f(x)=x^2-4\] would work \[(x+2)(x-2)\]

Answer 3

yes that looks good

Answer 4

okay awesome so that means g(x) could be \[g(x)=x^4+8\]

Answer 5

if 8 was a perfect square you could write it as y^2 where y is a whole number

Answer 6

wait i see that wouldn't work 8 isn't a perfect square.

Answer 7

and although x^4 is a perfect square (x^2 * x^2 is x^4)
it is NOT a quadratic (highest power is 2)

Answer 8

I could just change the - to + in the other function, right?\[g(x)=x^2+4\]

Answer 9

yes

Answer 10

okay thanks. Now I am really hung up on the last to functions I have to create.
The function h(x) is a perfect square trinomial.
The function j(x) can only have a GCF factored out of it.

Answer 11

a function with a perfect square trinomial is \[h(x)=x^2+2x +1\]
because (x + 1)(x + 1) = x^2 + x + x + 1 = x^2 + 2x + 1 and x^2 + 2x + 1
@phi

Answer 12

yes. (x+1)^2 (a perfect square) expands into the trinomial x^2 + 2x + 1

Answer 13

For
The function j(x) can only have a GCF factored out of it.

make up a quadratic function that does not factor example: x^2 + x + 1
and multiply every term by some number. The only way to simplify this is to factor out the number you multiplied by. Example: 5(x^2 + x + 1) = 5x^2 +5x + 5

Answer 14

@phi j(x)=4x^2+4x+4
would that work?

Answer 15

not sure if it matters but a sum of squares
"x^2 + 4"
cannot be factored

Answer 16

The function j(x) can only have a GCF factored out of it

Answer 17

yes, j(x)=4x^2+4x+4
works
you can factor out the 4
4(x^2+x+1)
but you can't factor x^2+x+1
into "nice factors"

Answer 18

thanks I am done I just wanted to double check what I put. Can you help me with something else?