further maths homework

[tough temple]

dont even know where to start

[slate void]

if x = -5 is the line of symmetry then you can find the second coordinate which also has y value 8. If you sub these two points into the equation given you will get 2 simultaneous equations in terms of a and b so then just solve for b

[tough temple]

so 9-9a + a^2 + b = 49-49a + a^2 + b

or what

im so confused lmao

also apparently this is wrong? but it seems right to me

to be fair, with pretty much all of these questions i havent got a clue

i mean what is this? we were never taught anything to do with this and now she suddenly expects us to know?

they literally just decided not to teach us any of this and now we're expected to know it? i've texted all my friends who take the subject and they also agree that we werent taught anything to do with this

bit strange idk

[humble oracle]

if x = -5 at the turning point then a = 5, then you can sub in the point (3,8) and solve for b

[humble oracle]

this is right but you didnt simplify fully

(w+4) - (w + 1) = 3

[tough temple]

that makes sense

[humble oracle]

so the answer is 3(w+4)^2

[tough temple]

what

how did you get there

[humble oracle]

mate you wrote it down

its right there 💀

you put (w+4)^2((w+4)-(w+1))

you can simplify the bigger bracket to just 3

[tough temple]

frick

[humble oracle]

basically if you have a quadratic in the form of a(x + b) + c

then the turning point is (-b, c)

[tough temple]

im not following

where did 3 come from

[humble oracle]

ok lets look at this question ^^

(w + 4)^2 * ( (w+4) - (w+1) )

[tough temple]

drfrostmaths has a stupid dumb system where if i submit the wrong answer i cant try again unless i complete all the other questions first

so i cant try that question again now lol

[humble oracle]

(w+4) - (w + 1) = w + 4 - w - 1 = 3

[humble oracle]

which one are you on

[humble oracle]

you see how the equation is in the completing the square form

[tough temple]

im aware that this whole thing is messy and yes it stresses me out too but i cant really do anything otherwise

[humble oracle]

do you know what completing the square is

[tough temple]

sort of

i mean i know it in regular maths

[humble oracle]

when the equation is in that form a( x + b)^2 + c for example

[tough temple]

but clearly i dont understand it well enough

[humble oracle]

the turning point is (-b, c)

[tough temple]

and i just need to know that i suppose?

[humble oracle]

so for this one b is 1 and c is 2

[tough temple]

is that just a piece of knowledge that we havent been given before

[humble oracle]

so the turning point is (-1, 2)

[humble oracle]

you dont need to know it for this question you can differentiate and set it equal to 0 and solve for x then sub x back into the orignial equation

but that is way longer to do

and not what your meant to do for this questoin

they gave it in the completing the square form

so you can just figure it out

[tough temple]

so the turning point is (-1,2)

[humble oracle]

yes

[tough temple]

ok

[humble oracle]

and for the points of intersection

sub in y = 0, for where it intersects the x-axis, and sub in x = 0, for where it intersects the y-axis

once you do all that you have 3 points which you can use to plot the quadratic

[tough temple]

but doesnt it intersect the y axis twice?

and how do i sub y = 0? i cant just plug it in, there is more steps to get there

also, how is turning point (-b,c) when surely a should affect it

how could A not affect the result? it changes the formula

[humble oracle]

i mean you can differentiate it if you want and set equal to 0 and solve for x and sub it back into y

you will get the same point

a does not affect the result

its just a given

well its not a given there is a reason i just cant be arsed to show you

one sec lemme see if i can find it

[tough temple]

i really dont see how you can sub in y

0 = -1/2 (x+1)^2 + 2

[humble oracle]

yep

then solve for x

whats the problem

[tough temple]

how can you just get -3 and 1 from that

what steps do you take

[humble oracle]

-2 = -1/2 (x+1)^2

[tough temple]

ok that makes sense

[humble oracle]

4 = (x + 1)^2

[tough temple]

yes that makes sense

[humble oracle]

x + 1 = +2, -2

x = 1, -3

[tough temple]

right

ok that makes sense

next question

up to you which one you want to tackle next, if any

also desmos kinda came in clutch there

[humble oracle]

this one

you didnt simplify the big bracket

you're very close to the answer

[tough temple]

ok

so

how do i simplify the big bracket

((w+4)-(w+1))

how can that be simplified

OMFG

I SEE THE LIGHT

YES

THAT MAKES SO MUCH SENSE

[tough temple]

I GET IT

I ACTUALLY GET IT

🔥

HOW DID I MISS THAT

[humble oracle]

thats what im sayin

[tough temple]

OK THATS EASY

[tough temple]

ok do you know any of the other ones

[humble oracle]

now this one

x=-5 at the turning point so you know that a = 5, sub in a = 5, and the point (3,8) so x= 3, y = 8

simplify and you should get the value of b

[tough temple]

i did that

i got b = 6

because 8 = (-3 + 5) + b

wait

yeah

anyway that was wrong

[tough temple]

im assuming you mean x = -3