Question

I will award a medal! I just need to know if I am doing this right.

Answer 1

Doing what right?

Answer 2

1.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 3

Yes, that's right.

Answer 4

this is what I have so far
Quadratic equation 1) f(x) = 2x2+3n4+5
Quadratic equation 2) g(h) = 3x4+9+10g2
Quadratic equation 3) h(x) = 25x2+3a2+4b4
Quadratic equation 4) j(x) = 24x+8b2+2a

Answer 5

are my equations right? Am I doing what the question is asking?

Answer 6

Yes, exactly!

Answer 7

okay thank you!

Answer 8

so now for equation 1) I just factor it?

Answer 9

No problem!

Answer 10

Yep.

Answer 11

okay makes more sense now :-) I really appreciate it!

Answer 12

I don't understand this
Quadratic equation 1) f(x) = 2x2+3n4+5

what is 3n4 ?
how do we know f(x) is a difference of squares ?

Answer 13

For
The function f(x) is a difference of squares.

An example would be: \( f(x)= x^2 - 9 \)
both \(x^2\) and 9 are squares.

Then demonstrate to him how to rewrite each function as a group of factors, if possible.

I think they want you to factor it. we know (a^2 - b^2) = (a+b)(a-b). Use that rule to factor f(x) to get
\[ f(x)= x^2 - 9 \\ f(x)=(x+3)(x-3) \]

Answer 14

OOH! okay! Thank you!

Answer 15

I had forgotten how to factor the difference of squares

Answer 16

can you do
The function g(x) is a sum of squares.

?

Answer 17

I actually need help with that. I changed my exuation for g(x) to X^3+N^3

Answer 18

Can you walk me through please

Answer 19

I think it is ok to use numbers instead of N

but remember this: if f(x) is a quadratic, that means it has a term a x^2 where a is any number (except 0)
there are no x terms with a bigger exponent than 2.
it might have x terms with smaller exponents of 1 or 0 (x^0 is 1)

you say
*** g(x) to X^3+N^3 ***

that is not correct: a quadratic does not have an x^3 term

Answer 20

oh okay. So could it be X^2+N^2?

Answer 21

yes,

Let's choose N= 2, so you can say
g(x) = x^2 + 4

that is a sum of squares.
it will not factor.

Answer 22

so a sum of squares can't be factored?

Answer 23

yes, a sum of squares does not factor

Answer 24

The function h(x) is a perfect square trinomial.

the way to do this is start with h(x)= (x+4)(x+4) (the factored form)
multiply it out to get the "trinomial"

Answer 25

oh okay. I just wrote that down. It doesn't factor because you can't find the GCF right?

Answer 26

right

Answer 27

so use distributive property?

Answer 28

?

Answer 29

nevermind sorry. I was confused for a second. Is the equation I have right for the perfect square or do I need to multiply instead of add?

Answer 30

sorry algebra is confusing for me

Answer 31

I don't think we need to use a's, b's and n's. Just x and numbers

to find a perfect square quadratic, start with h(x)= (x+ 4)(x+4)
(or any number you want instead of 4)
now multiply (x+4)(x+4)
can you do that ?

Answer 32

yeah. If I did it right, I got x^2+8x^2+16

Answer 33

So, when doing my work, My very first step would to be to come up with a functi. That function would be (x+number) times (x+number) right? Then I solve for the trinomial. What next?

Answer 34

depends what kind of quadratic you want.

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

this one could be 4x^2 + 4x + 4
you can factor out a 4: 4(x^2+x+1)
but x^2 + x +1 won't factor, so that is as much as you can do .

Answer 35

oh okay. So then since that is all you can do, is that your answer?

Answer 36

yes, that is the last question

Answer 37

That is what I did for the equation I had so I think I had my work right but the equation was wrong.

Answer 38

can you give me a second? I have one more I need help with

Answer 39

*** you had Quadratic equation 4) j(x) = 24x+8b2+2a ***
notice there is no x^2 term so j(x) is NOT a quadratic
8b^2 + 2a should not be there. just numbers or a simple x term
if you made it
j(x) = 24 x^2 +8x + 2
that would work: 2 ( 12x^2 +4x +1)
and we can't factor anything else out.

Answer 40

Oh okay! I will fix that. Can you give me another example of a function with the difference of squares? I want to make sure I know that.

Answer 41

a difference of squares means you need two squares (something multiplied by itself)
that you subtract.

one of the squares has to have x^2 (so that you have a quadratic)

so you could use (3x)^2 and 20^2
now square both, and subtract
9x^2 - 400

is the difference of two squares

Answer 42

Okay thank you! Everything makes much more sense now! Thanks for all of your help :-) I wrote down the examples you gave me and took notes so I have it for the future.

Answer 43

Thanks for the medal!