quartic curves

[potent rose]

I am doing summer bridging work to start year 12 this September; it says that if a factor is repeated then it only touches the x axis at that point. Can someone help explain to me why that’s true?

[mellow sedge]

,rotate

[supple escarp]

i acc dk why

[pseudo pond]

i dooo

Alr so basically

You see

[potent rose]

If you repeat the factor twice then for a quartic curve - all the x intercepts are going to be idk for example

3

3

1

7

and the double three means that the curve touches it

Only thing is I got no clue why😭

WAIT

No

I am so lost

Why did my ass choose maths alevel 😭😭

[supple escarp]

no ur right

[potent rose]

Maybe cause it goes through it twice

That means

Causes it to make that shape

[supple escarp]

dw u dont need to know y this happens 😭

[supple escarp]

yh if its an even number of roots at the same point

but idk why

im trying to think of it in terms of transformations

idk if thats getting anywhere

[supple escarp]

if u think ab (x-3)^2 on its own thats a quadratic in completed square form
and the vertex of (x-a)^2+b is (a,b) and the vertex is a turning point which is what the graph is doing here

idk 😭

[potent rose]

Nah I get what you mean

[supple escarp]

multiplying (x-3)^2 by (x-a) for any a doesnt change the position of the 3 root

so (x-3)^2(x-1) the vertex is in the same spot?

[potent rose]

Yeah okay I think I get it!

Thanks!

[supple escarp]

omg im a genius

[potent rose]

Does this server have a thanking bot

[supple escarp]

😭

no dts

[potent rose]

Damn I swear there was one 😭

[supple escarp]

can u do /close

[potent rose]

Ofc

Oh

How do I close this

It’s not letting me

[supple escarp]

nvm that wasnt right

js leave it

[sturdy moon]

dumb

[supple escarp]

how do u close it

[sturdy moon]

alt f4