I have no clue what to do 😭

[restive coyote]

Please help me (ITS SIX MARKS 😭)

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[pale hollow]

are you in a test

if yes u can get quicker help

with the fasthelp section

[restive coyote]

No it's formal homework so fancy homework

[brittle stream]

i didnt know theres one

[brittle stream]

i changed to spectre armor

ok OFF TOPIC

sry

[pale hollow]

cuz there isn't

i was baiting him to say yes

[brittle stream]

i knew smth was off

ANYWAY

[restive coyote]

Please help 🙏 been at that question for literally hours 😭

[brittle stream]

id start by finding the roots. what have you done so far? any progress?

the roots are just the x intercepts

[restive coyote]

I can't remember how to do that and my notes where no help

[brittle stream]

THIS IS WHY YOU NEED TO TAKE GOOD NOTESS IN CLASSS

WHAT IS WRONG WITH PEOPLE

anyway

x intercepts are where y = 0, so

[restive coyote]

😭

[brittle stream]

either 16+6x−x^2=0 or −x^2+6x+16=0

[brittle stream]

typical highschooler

even us ms students have more wisdom apparently than 50% of hs students

[brittle stream]

THIS

we rewrite

[restive coyote]

I might have been off during that time due to some personal stuff don't blame me 😭

[brittle stream]

into x^2−6x−16=0

[brittle stream]

idk highschool ok??

idk what they let you do

idk what they dont let you do

idk what freaky ahh things people do

i dont WANNA KNOW ok?

[restive coyote]

OKAYY 👌 completely understand wasn't going to say 😭

[restive coyote]

Then what?????

[brittle stream]

Solve this quadratic equation using the quadratic formula

it becomes x = (-(6) ± sqrt((-6)^2 - 4(1)(-16))) / 2

better representation

[restive coyote]

Okayy then what????

[brittle stream]

Here, a=1, b=−6, and c=−16

it becomes

x = (6 ± sqrt(36 + 64)) / 2

then 36+64 is obviously 100 and sqrt 100 is 10

so

x = (6 ± 10) / 2

so x = 8 or x = -2

[restive coyote]

So they are the roots???

[brittle stream]

sorta

point A: A(8, 0). Point B: B(-2, 0)

[restive coyote]

How is A 8 but it's on the left side of the y axis

[brittle stream]

mixed them

[restive coyote]

Okayy

[brittle stream]

Ooookay gotta go to school now bet

(its 7 am)

sry

[restive coyote]

No no it's okay thank you so much, hate time differences 😭 good luck for schooooll

[severe laurel]

Sstill need help?

[restive coyote]

Yeah pretty much I am so confused, my friend sent me her working so I am trying to work of it slightly yk

[severe laurel]

alr lemme rep0ost the image real quick

have you learnt differentiation yet?

[restive coyote]

I don't think so? Idk

[severe laurel]

timesing by the power and reducing it by one? ring any bells? its ok if not

[restive coyote]

Nah I don't think so

[severe laurel]

alright so well save D for last

for A and B, these are known as the roots

you can tell they are the solutions to the eqn: 16 + 6x - x^2 = 0

because y = 0 at these points

so as you were shown by spectre, you can rearrange it into x^2 - 6x - 16 = 0

[restive coyote]

Yeahhh

[severe laurel]

now you can solve for x in two ways, the quadratic formula, or factorising (splitting into two parts)

[restive coyote]

I trying to do the factorising but my friend got a different answer so I am confused on who's right or wrong or just wrong

[severe laurel]

ok so to factorise, you need to numbers that add up to -6, and multiply to -16, and by thinking about it for a minute, you can see -8 and +2 fit this criteria

so now you can rewrite the equation to get: x^2 + 2x - 8x - 16

[restive coyote]

Wait how is it -8 +2 not +8 -2

[severe laurel]

-8 + 2 = -6, whereas 8 - 2 = 6

[restive coyote]

I thought it was just 6 though

[severe laurel]

remember, we transformed our expression into x^2 - 6x - 16

and you have to include the negative

you can think of it as x^2 + (-6x) + (-16) if that helps

[restive coyote]

Oooooh okay cause the numbers =0 instead of it being the y= the numbers

[severe laurel]

uh kinda yeah

so if we have x^2 + 2x - 8x - 16

we can factorise the first two terms (x^2 + 2x) into x(x + 2), and we can factor the second two terms (- 8x - 16) into -4(x+2)

[restive coyote]

Alrightt

[severe laurel]

so now we have this expression: x(x+2) -4(x+2), and now we can see that (x-4)(x+2) = 0

and that can be a difficult step but it works because if you think about it, expanding (x-4)(x+2) is the process of multiplying (x+2) by x, and then by -4

and for (x-4)(x+2) = 0 to be true, either (x-4) = 0, or (x+2) = 0 because anything multiplied by 0 is 0

[restive coyote]

Does the 4 go to X=+4 and the 2 go to X=-2 ?

[vital bane]

Hey just a question did you change the sign

[severe laurel]

yeah nice there are your roots, and it's obvious that A is -2 and B is 4

[severe laurel]

yeah he did by multiplying both sides by -1, or moving everything to the other side but it would have worked if he hadnt

[vital bane]

Maybe he learned the formula for the top of a parabola -b/2a

[vital bane]

Ok ok

[severe laurel]

maybe idk i haven't even learnt that

[vital bane]

Just a product of differentiation

[severe laurel]

i just tested it, maybe

@restive coyote , so now you have A and B, we can do C next as it's very easy

[vital bane]

@restive coyote good luck

[restive coyote]

Thank youu

[restive coyote]

How do you do it, is that the thing you change something to 0?

[severe laurel]

yeah so lemme remind myself of the quadratic

16 + 6x - x^2 = y

ok

so if a point is on the y axis, then the x co-ordinate must be 0 (obviously)

so we can plug in 0 to find y

16 + 6(0) - 0^2 = y

16 + 0 + 0 = y -> y = 16

so we can tell the y intercept ( or c ) is at (0, 16)

[restive coyote]

Okayyyy

[severe laurel]

alright, now D

do you remember learning anything about a formula -b/2a

[restive coyote]

Mmmm i can't remember maybe

[severe laurel]

how about completing the square

its when you turn a quadratic of the form ax^2 + bx + c into the form a(x+b)^2 - c

[vital bane]

I think they want us to use the symetry there

If nof formula

[severe laurel]

i have actually never ever thought to use symmetry to find a maxima

thats gotta be alot easier too

[vital bane]

I've used it a lot very helpful if u are speeding through

[severe laurel]

alright we're using symmetry xd

i hate completing the square, and teaching it seems even harder tbh

[restive coyote]

I can't use it cause my teacher will get annoyed 😭

[severe laurel]

noooo

[restive coyote]

We never did that before

😭 sorry

[severe laurel]

ill just rq explain what you could do with symmetry to find it, you would find the x coordinate in the middle of your two roots (a and b) and plug it into your oringinal equation to find the y

but completing the square works too

our expression is: 16 + 6x - x^2 = y
we can rearrange this to:
y = -x^2 + 6x + 16

[restive coyote]

Okayy

[severe laurel]

we can factor a negative out of the first two terms, to make x^2 positive (it just makes it alot easier to work with)

[restive coyote]

Okayyyy

[severe laurel]

this next step isnt as easy to understand, but trust it makes sense.

inside the bracket,

we turn it into (x-3)^2 - 9

like this

and lemme explain this rq

note that (x+a)^2 = x^2 + 2ax + a^2

and we want to "reverse" this and go back into (x+a)^2 form

we know that the bracket will be (x+a), and to get a -6x, a must be -3, because 2 * -3 * x gives us -6x

but if you just want to memorise, you half the number infront of an x

[restive coyote]

Alrighttt

[severe laurel]

i forgot to say, but the -9 is because of the a^2 here

lmk once u have compreheneded this bc it took me a minute to understand the process when i first learnt

[restive coyote]

Idk if I will get that I just tried to follow what my friends did 😭

[severe laurel]

wheres the working for D

[severe laurel]

i mean it's right

[vital bane]

Symmetry

[vital bane]

Top right

[restive coyote]

The f(3) thing and the thing that's like 8+(-2)/2

[severe laurel]

wait

okay you got D right

but we got B wrong lol

[restive coyote]

How lol 😭

I thought it was +4

[severe laurel]

heres' the error

[severe laurel]

your working for D depended on B being equal to 8, because you found the point inbetween our two roots with (B + A)/2 and you knew that the maximum value would be there, because a parabola is symmetric

my fault

[restive coyote]

So is it eight???

[severe laurel]

yeah B is 8

[restive coyote]

Ohhh okayyyy, thank you so much you genuinely help me so much thank you 😭😭<3

[severe laurel]

no wirries have a good night

[restive coyote]

You toooo

[wooden canopy]

@restive coyote

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