Question

evaluate the function f(x)=X^2+8x+9 at the given values of the independent variable and simplfi
a) f(3)
B)F(x+2)
c)f(-x)

Answer 1

So you've got your function \(\ f(x)=x^2+8x+9\) and your problem is basically telling you when you have values of \(\ x= 3, x+2, -x\) what would your function be?

All we have to is plug in all these x-values in place of your function and simplify it :)

Answer 2

let's start with (c) , when f(-x) = x^2 +8x+9

For this one, all we have to do is replace the x with -x and simplify it.

f(-x) = (-x)^2 +8(-x) + 9

Can you simplify this for me?

Answer 3

x =3^2+8(3)+9
a=42

Answer 4

Yess good job. you got this! :)

Answer 5

now I am working on the b
and it the equation is f(x+2)=(x+2)^2+8(x+2)+9

Answer 6

and remember, f(x) = y so essentially, f(x) is a function of x, therefore we can rewrite this problem as : y(x) = x^2 +8x +9

Answer 7

And you are absolutely correct for (b)

Answer 8

\(\ (x + y)^2 = x^2 +2xy + y^2\) , use this when expanding the first part o your function :D

Answer 9

I mean expand it using this form* if you were stuck on that!

Answer 10

figging hate this darn stuff cuz it just confuses me

Answer 11

What part is confusing you? I'll see if I can help you clarify that :D

Answer 12

the x+y were does y show up in the equation

Answer 13

Oh I meant \[\ (\color{blue}x + \color{green}y)^2 = (\color{blue}x + \color{green}2)^2\] I was showing you that if you followed my expansion for (x+y)^2 you can use the same method for expanding (x+2)^2 :)

Answer 14

and i'm just setting these two equal to eachother to show how the equations math up, not saying they are equal to eachother., haha.

Answer 15

ok I understand now

Answer 16

Maybe I should have written it... \[\ (\color{blue}x + \color{green}y)^2 =\]\[\ (\color{blue}x + \color{green}2)^2=\] Yeah that's what I meant when I was saying a comparison, haha,.

Answer 17

ok ty sorry I get really frustrated with complex forumlas

Answer 18

Oh no problem. What did you get for the (b) and (c)?

Answer 19

im still tryi8ng to figure out b

Answer 20

Ahh, what do you have so far for b? :3

Answer 21

2that the (x+2)^2 is (x+2)(x+2)+8(x+2)+9

Answer 22

ok, and if (x+2)^2 = (x+2)(x+2), do you know how to use the foiling method? :o

Answer 23

i forgotten it long ago and had trouble with it when i used it in my last math class a year ago

Answer 24

Ah, ok. FOIL stands for First, Outter, Inner, Last. Let's approach this step by step.

Answer 25

so one would be 5x and the other is also 5x right

Answer 26

Can you explain to me how you got the 5x?

Answer 27

not five I am looking at the example it would be 2x and 2x sorry

Answer 28

Well, I guess that is part of it. :) you're on the right track! Let's approach this using the FOIL method so if you come across another polynomial of this type, you'll understand how to properly expand it :D

Answer 29

\(\ (\color{blue}x + \color{green}2 )^2 = (\color{blue}x + \color{green}2)(\color{blue}x + \color{green}2)\)

1. First : \(\ (\color{blue}x +2)(\color{blue}x +2) = \color{red}{x^2}\)
2. Outter : \(\ (\color{blue}x +2)( x + \color{green}2)= \color{red}{2x}\)
3. Inner : \(\ (x + \color{green}2)(\color{blue}x + 2) = \color{red}{2x}\)
4. Last: \(\ (x +\color{green}2)(x+\color{green}2) = \color{red}4\)

Adding these all up together, we get: \(\ \color{red}{x^2 + (2x + 2x) + 4} = x^2 + 4x + 4\)

Answer 30

Now following the colors and the acronym FOIL, can you see what multiplies with what and how I get my results? :o

Answer 31

but its not 4 its 8

Answer 32

Which part are you referring to? Sorry, i'm a bit confused D:

Answer 33

you said it s x^2+(2x+2x)+4 when the 4 should of been 8x I think

Answer 34

Nope! :D I just helped you expand the first PART of your function, when f(x+2) = x^2

So when you plug in (x+2) for x^2 you get (x+2)^2

and (x+2)^2 = x^2 +4x + 4 :D

Answer 35

Now you've for your other 2 parts, the 8(x+2) + 9 :P

Answer 36

would the equation look like 2x+2x+8x+16+9

Answer 37

I don't think so D:

Answer 38

Well, let's see. do you understand how (x+2)^2 = x^2 +4x + 4 came to be when we expanded the polynomial? If you follow the foil method I posted a few posts up, that should help a bit!

Answer 39

not really I see how you do it but dont understand where you get the four terms from

Answer 40

Hmm..alright.

The first term comes when we multiply the "first" terms of EACH multiplier. that is, we multiply the x to the x. Are you with me? :D

Answer 41

yes

Answer 42

Ok, that is our FIRST term.

Our second term comes when multiply the "outer" numbers. We take the "x" from our first factor, and multiply it to the "outer" number, "2", therefore we get 2x.

Let me know when you understand this as well :3

Answer 43

i understand how you get the 2x+2x but from there is were i get lost

Answer 44

Oh, add the 2x + 2x together because they are like-terms :D therefore you get 4x!

Answer 45

I put parenthesis () around them to group them together, letting you know they were like-terms and needed to be added together :P

Answer 46

ok so that is were we get the x^2+4x+4 from right
so were does the 8(x+2)+9 come in

Answer 47

i am really sorry that you are having to give up so mcuh time to help me with this equation

Answer 48

because your main function is f(x) = x^2 + 8x+ 9, we only solved the x^2 part.

You're evaluating your main function when f(x) = f(x+2), so now you have to expand 8(x+2)

Answer 49

Oh no! it's ok, don't apologize xD as long as you understand how to solve other questions like this I'll be happy :)

Answer 50

Basically we replaced ALL your ORIGINAL x's with (x+2)'s.

Answer 51

the 8(x+2) would be 8x+16 right

Answer 52

Mmhmm :)

Answer 53

so the whole equation would look like x^2+4x+4+8x+16+9 and combine like terms

Answer 54

Yes! you got it :D

Answer 55

so the answer is X^2+12x+29

Answer 56

You got it :)

Answer 57

do you have time to help me with part c

Answer 58

For (c) we're just replacing all the x's in your original function with -x

Answer 59

so it'll be f(-x) = (-x)^2 + 8(-x) + 9

simplify this and you'll have your answer here too :)

Answer 60

ok so (-x)(-x)_8x+9 correct

Answer 61

(-x)(-x)-8x+9

Answer 62

mmhmm, and when you multiply (-x)(-x) you get?

Answer 63

+x

Answer 64

x^2-8x+9

Answer 65

You got it :)

Answer 66

ty I tryed to fan you but I can not right now I will when I can

Answer 67

Thanks! :D