Question

cubic functions

Answer 1

Find a cubic function with the given zeros.

7, -3, 2

Answer 2

@Luigi0210 @halorazer

Answer 3

Well do you know what the definition of a zero is? :p

Answer 4

yeahh its where the graph goes all funky. i just dont know how to make an equation out of that :P

Answer 5

No, it's where the graph intersects the x intercept.

Answer 6

x axis*

Answer 7

Work backwards.

Answer 8

.-. but i cant graph anything above ^2......

Answer 9

She obviously doesn't know how to do that brotaco.

Answer 10

It's no different than any other zero. It could be a polynomial of the 69th degree and it would still work.

Answer 11

lol 69..... mind in the gutter..... but no it dosent my calculator refuses to accept it

Answer 12

No, no. No no no. You're supposed to find an equation, not the value.

Answer 13

.-. what

Answer 14

It's essentially factoring the polynomial then setting it equal to zero. For example, if we had y=x^2-4
We'd factor it as (x+2)(x-2)
Then we'd take the factors individually and set them equal to zero.
x+2=0
-2 -2
x=-2, meaning x would hit the x axis at (-2,0)
And then on the other hand we have x-2=0
and we'd add two
x=2, meaning it hits at 2,0. Make sense?

Answer 15

where did you get y/x^2-4?! O.O

Answer 16

It was a random function that I chose.

Answer 17

oh.... okay...... so this one will hit at (0,7) (0,-3) and (0,2)?

Answer 18

No.

Answer 19

-.- you just told me that thats what happens

Answer 20

Try flipping the signs on all of them. That's what I said happens.

Answer 21

x+2=0
-2
it would hit at -2,0, even though it is (x+2)

Answer 22

If 7, -3, 2 are the zeroes of a cubic function, then

x = 7
x = -3
x = 2

Placing all terms on one side you have:

x - 7 = 0
x + 3 = 0
x - 2 = 0

Observe that x - 7, x + 3, and x - 2 are linear factors and the zero product property can be applied:

(x - 7)(x + 3)(x - 2) = 0

We stated from the beginning that these were zeroes of a function which we can call f(x) so

(x - 7)(x + 3)(x - 2) = f(x)

Answer 23

Expand the left side to write the cubic polynomial in descending order.

Answer 24

your going really fast .-.

Answer 25

You can always read the information at your own pace.

Answer 26

He's basically saying foil out the (x-7)(x+3)(x-2) so it is a single function.

Answer 27

now that makes sense, i forgot who it was but one of the administrators are like alti foil .-.

Answer 28

*anti foil

Answer 29

I explained every step in the simplest, most logical possible manner. I left the final step for you which is to simply multiply the factors.

Answer 30

soooooo its like
x+3
x-7
----
-7x-21
x^2+3x+0
----------
x^2-4x-21
x-2
----------
-2x^2+8x+42
x^3-4x^2-21x+0
----------------
x^3-6x^2-13x+42

Answer 31

It looks like you did it correctly, yes.

Answer 32

yay c: now one of you give the other a medal and ill give one of you a medal c: cuz you both helped and deserve a medal ^.^

Answer 33

Tbh he did more work than I did.

Answer 34

@lovelyharmonics, the way OS works is, you give the medal for the Best Response.

Answer 35

There's no need to negotiate about who will give whom a medal.

Answer 36

i know .-. but you both helped and its mean to not do that

Answer 37

common bro other administrators are fine with that :P

Answer 38

There's nothing mean about showing your appreciation for the help you received.

Answer 39

Help does not have to be singular.

Answer 40

yes, i do appreciate people helping but i wish i could give out multiple medals but sadly i cant for this website has major issues with "teamwork" and thinks 1 person should come out on top.... but both of you help equally and since i cant give multiple medals one of you give the other a medal and i will give the other person a medal .-.

Answer 41

I gave @halorazer a medal per your request, but you don't understand how this works. Medals do not hold equal weight. The medal of the original poster holds more weight than any other medal given.

Answer 42

.-. huh well a medals a medal in my mind c: and thank you all ^.^

Answer 43

okayyyy so Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

2, -4, and 1 + 3i
for this it would be (x-2)(x+4)(x-1)(x-3i)

Answer 44

i^2is -1 right?

Answer 45

1 + 3i acts as one zero and its conjugate is 1 - 3i, which is another zero of the polynomial.

So expanding (x - 2)(x + 4)(x - 1 - 3i)(x - 1 + 3i) will yield the correct polynomial expression of the desired function.

Answer 46

okay so
x-2 *x+4=
4x-8+x^2-2x+0=
x^2+2x-8

Answer 47

and
x-3i*x+3i=
3ix+9i^2+x^2-3ix+0=
x^2-9

Answer 48

youre way seems like its 5x as hard

Answer 49

Actually, what I meant to do is this:

\(((x - 1) - 3i)((x - 1) + 3i) = (x - 1)^2 - (3i)^2\)

Answer 50

If you remember difference of squares:

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

Answer 51

.-. hey i gtg to bed cuz its 11 im sorry :c but thank you for helping c:

Answer 52

Good luck