Polynomial function

[ebon sable]

I was asked to solve the pic titled "activity 2" using the process I posted below. But somehow with the plotting points I calculated it seems the graph o formed isn't a polynomial function I don't know where I went wrong or what to do, pls help.

[stoic mesa]

First off the y int isnt 0

[ebon sable]

Are you referring to point c in the graph I calculated?

These are my answers to that table

[stoic mesa]

If you wanna make a polynomial on there pretty sure u have to actually input the function

[stoic mesa]

Yes it’s supposed to be (0.-6)

[ebon sable]

Can u explain further? Iam still confused

[stoic mesa]

Well if u plug in 0 you get -6

[ebon sable]

I did get the 0,-6 in solving for step 2 at the activity but on the example the calculated y-int in step two wasn't used further into step 3 and 4

Step 3, the table. And number line I probably got lost there

[stoic mesa]

U made some errors on the table

How is the first interval below if you get a positive number

[ebon sable]

Oh sorry, I didn't clarify I ignored the below and above in the table cus if my calculations would be correct I would know either way and place it onto my final paper. It's really the numbers that confusing me specifically the intervals🫠

Did you see some errors in the calculations of the numbers? Pls tell me if you do

But I did try to double check everything

[stoic mesa]

What’s confusing?

Like how you find the intervals?

[stoic mesa]

First part is supposed to be 2x(-4)^3+3x(-4)^2-11(-4)+6

Forgot I can’t use * on discord

[stoic mesa]

Which is not 10.5

[ebon sable]

But substituting it wasn't in the picture the teacher sent

Lesson picture(?) The teacher sent

Iam confused abt the whole thing at this point

The teacher never gave lecture

[stoic mesa]

Oh

[stoic mesa]

Ur supposed to do that for the factors

And then multiply them out

[ebon sable]

I used the synthetic for the factors tho

It's on the lesson pic

[stoic mesa]

Ok so for the calculating whether it’s above or below input it into each factor then multiply them out

For example we have a factor (x+3)

Input -4 we get -1

Then do it for the rest of the factors

And then multiply them all out and then by 2 but that doesn’t really matter since it’s positive

U got the factor right

[ebon sable]

Factors I got were 2, -3 and -½

[ebon sable]

Substitute each test value to the P(m)?

[stoic mesa]

Yes so you input them all into (x-a) where a is a specific zero and then multiply them all out

[stoic mesa]

You could do that too

Since it’s the same thing

[ebon sable]

What would I be answering if I do that? Would it be the point?

[stoic mesa]

You are seeing if the graph is positive or negative on that interval

You check in between the zeroes because before and after zeroes are when the graph can change signs

[ebon sable]

Iam still so confused, what? 😭 sorry let me take a step back. Within in the table what was the error that will be fixed by the substitution? The substitution part really isn't in the lesson notes the teacher sent..

[stoic mesa]

It somewhat is

[ebon sable]

You mean to say -6 was substituted into the p(×)?

For double checking or to get the plot points?

[stoic mesa]

So the polynomial can be written as (x-1)(x-2)(x-3) and you input the number into each of the factors and multiply them out, basically inputting the value

[stoic mesa]

No

Since you got (0,-6) you’re good on that part

But when you input -4 you don’t get 10.5

You got the zeroes 2,-3,-1/2

so the polynomial can be written as 2(x-2)(x+3)(x+1/2)

Input -4

You get a negative number

[ebon sable]

So I probably had some errors in calculating there?

[stoic mesa]

Yes

[ebon sable]

If I recheck that rn. Would that effect all other plotting points?

What if it's still wrong after? W8

[stoic mesa]

If you have the zeroes, signs right, and the y intercept right I think you will be fine

The thing says to do exactly that

[ebon sable]

I really 10. 5...

[stoic mesa]

Did you apply the exponents to -4

[ebon sable]

Yes

W8 ill recheck again

[stoic mesa]

If you just plug it into the factors you g should get a negative times negative times negative

which is negative

[ebon sable]

Substituted it, and got -42

Isn't that to big?

[stoic mesa]

Nah it’s good

[ebon sable]

What do I do with it?

[stoic mesa]

Wait r u sure u got the zero -3

I plugged it in and I dont think that’s right I’ll check again

[ebon sable]

But if I use this it really is 10.5

[stoic mesa]

I wait nvm

It’s my fault

[stoic mesa]

?

Do you know what they did to get -6?

They multiplied all of the factors

(0-1)(0-2)(0-3)

That’s what they did

[ebon sable]

Multiply?

Not add?

👁👄👁

[stoic mesa]

Yes

[ebon sable]

W8🖐

[stoic mesa]

It’s just that multiplying is the same as adding for that those numbers

[ebon sable]

Huh I multiplied it

On this table I multiplied it and got new plot point

(-4,21) , (-1, -3) , (0,3) , (3,-2)

I'll try plotting to see

[stoic mesa]

Didnt you just get -42 from -4 tho

[ebon sable]

Idk either if use the table it just don't get -42

Idk no more

[stoic mesa]

I’ll p

This is what it should look like

[stoic mesa]

Table should look like this

Then multiply them all out and multiply by 2

[ebon sable]

Did u use the function itself here?

[ebon sable]

At what part of the table is this?

[stoic mesa]

Yes

But u could draw something similar with just the info of signs and zeroes

[stoic mesa]

It’s this circled part

But for the function u were assigned