Question

If f(x)=7x-5x^2, then find each of the following:
A.) f(3k-7)
B.) f(x+h)
C.) f(-4k^5)

Answer 1

You simply plug in 3k-7 in place of every x and simplify

f(x) = 7x - 5x^2

\(f(\color{red}{3k - 7}) = 7(\color{red}{3k-7}) - 5(\color{red}{3k-7})^2\)

Answer 2

Okay that makes sense! Will you check my answers when I'm done?

Answer 3

A I got -14

Answer 4

Sure! :)

Answer 5

We have variables, how did you get rid of them? Can you show your work so I can see where you went wrong? (:

Answer 6

I used my calculator, guess that doesn't work lol. Let me work it out

Answer 7

Okay I'm stumped

Answer 8

to expand (3k-7)^2

use the formula

\(\Large (a-b)^2 = a^2 - 2ab + b^2\)

and to open up 7(3k-7)

use the distributive property which states a(b-c) = ab - ac

Answer 9

and after you expand (3k-7)^2 don't forget to distribute the -5 ;o

Answer 10

I ended up with f(3k-7)= 21k + 76. I feel like that's not right

Answer 11

Do I need to use that formula for 7(2k-7)?

Answer 12

no, you need to use the distributive property for 7(3k-7)

psst, it's 3k not 2k

and that's not right either

can you show your work? :p

Answer 13

I think I'm doing this all wrong :(
Okay f(3k-7) = 7(3k-7) -5(3k-7)^2

(3+7)^2 = 3 - 2(3)(-7)-7^2
10^2 = 3 + 42 - 49
100/-4 = -4/-4
-25
-5(-25) = 125

Then
7(3k-7)
21k - 49

-49+125+21k
76 + 21k

Answer 14

"(3+7)^2 = 3 - 2(3)(-7)-7^2"

it's 3k -7, and I don't know what formula you're using o.o
try this
(3k-7)^2 = (3k)^2 - 2(3k)(7) + 7^2

what do you get?

Answer 15

3k^2 - 6x + 35

Answer 16

\((ab)^m = a^mb^m\)

so what is \( (3k)^2 = ?\)

and you changed k to x and you didn't multiply 2 * 3 and 7 properly

and 7^2 is not 35

Answer 17

I thought 3k^2 just stayed like that?
My bad in multiplied 7 by -2 :(
Here's what I did

(3k)^2 - 2(3k)(7) + 7^2
3k^2-6k -14 +49
3k^2 - 6k + 35

Answer 18

7^2 = 7 * 7 = 49

\( (3k)^2 = 3^2k^2 = 9k^2\)

and
2(3k)(7) = 42k

sooooo

(3k-7)^2 = 9k^2 - 42k + 49

do you understand? o:

Answer 19

That makes a lot more sense. So sorry for the confusion, math isn't my strong subject /:

Answer 20

so what is

-5(9k^2 - 42k + 49)

distribute the -5

an extension of the distributive property
a(b - c + d) = ab - ac + ad

Answer 21

-45k^2 + 210 -245?

Answer 22

yesss, but you dropped the k after 210

and what is

7(3k-7) = ?

Answer 23

Oops typo!

7(3k-7)
21k - 49?

Answer 24

yes, now

21k - 49 -45k^2 + 210 -245 = ??

simplify it by adding/subtracting like terms

Answer 25

-45k^2 + 21k -84

Answer 26

oops, my bad

21k - 49 -45k^2 + 210k -245 = ??

I forgot to put the k after 210 ;p

Answer 27

You're good! So -45k^2 + 231k - 294

Answer 28

bingo!

Answer 29

You're amazing! Would I set b up the same way

Answer 30

yes, instead of 3k-7, you would use x + h

Answer 31

So f(x+h) = 7(x+h) - 5(x+8)^2

Start with (x+h)^2 = x^2 - 2(x)(h) + h^2 right?

Answer 32

yep

and then distribute the -5

Answer 33

Okay I got -5x^2 - 5h^2 + 10xh

Answer 34

so we have so far

7(x+h) - 5(x+8)^2

7(x + h) -5x^2 - 5h^2 + 10xh

now do 7(x + h)

Answer 35

7x + 7h

Answer 36

7x + 7h -5x^2 - 5h^2 + 10xh
now simplify (:

Answer 37

Can that be simplified?

Answer 38

The only thing I could think to do would be 24xh -5h^2 - 5x^2

Answer 39

it can't be simplified :b

you can't add h + h to make h^2

only h * h = h^2

h + h = 2h

but we can't simplify anymore :)

Answer 40

Okay so it stays how it was?

Answer 41

yeah xD

Answer 42

You tricked me lol. So for c do we still use the whole (a-b)^2=a^2-2ab+b^2 thing?

Answer 43

nope, C is much more simpler xD

Answer 44

Okay so 7(-4k^5) = -28k^5. Do the same to the other side?

Answer 45

yeah, but we first have to square it :)

Answer 46

400k^10?

Answer 47

nooo

\((-4k^5)^2 = (-4)^2(k^5)^2\)

hint: \( (a^b)^c = a^{bc}\)

Answer 48

16 and k^10? Or would it be k^7?

Answer 49

k^10 is correct

and then 5 * 16k^10 = ?

Answer 50

80k^10!

Answer 51

So the answer is 480k^10?

Answer 52

we can't add -28k^5 and 80k^10

and not sure how you got 480 o;

Answer 53

Shoot idk where I got 400k^2 from lol. I added that. So 80k^10-28k^5

Answer 54

xD

Answer 55

Thank you so so much for explaining that! Sorry it took so long

Answer 56

It's alright! Have a great day (: