/sci/ - Science & Math

[Anonymous No.7133342]

can someone please explain to me

f(x) = -x^2+6x-15

the vertex according to the book is (3,-6), i cannot get that fucking 6 negative and i cant figure out why.

Changing it to f(x)=x^2-6x+15 leads me to
y-15=x^2-6x
y-15=x^2-6x+9
y-6=x^2-6x+9
y-6=(x-3)^2 which is (3,6)

OR if i go y+15=-(x^2-6x)
y+15=-(x^2-6x+9)
y+24=-(x-3)^2 which is not (3,-6) either

What the fuck is wrong here?
why doesnt the first method work?
And what am i doing wrong in the second method?
thanks for the help i really appreciate it, its driving me nuts.... i know im a dumbass

[Anonymous No.7133344]

>Changing it to f(x)=x^2-6x+15 leads me to

you forgot to multiply f(x) by negative one with the rest of the equation.
-f(x)=x^2-6x+15

[Anonymous No.7133346]

I find your lack of algebra skills disturbing

[Anonymous No.7133355]

i know im retarded, thanks

so it would change to
-y=x^2-6x+15? then
-y-15=x^2-6x

How would i then get the y positive?
does -y-15 = y+15?

I would end up with 24 again on the y side wouldn't i?

I feel like im just totally missing something here

[Anonymous No.7133365]

going through it again with
-y-15=x^2-6x
i get
-y-6=(x-3)^2
I think i can turn that into
Y+6=-(x-3)^2 right?
which gives me the -6 i need but wouldnt that turn -(x-3)^2 into (-x+3)^2 and give me (-3,6) which is still wrong?
what the fuck am i missing

[Anonymous No.7133368]

>>7133342
>being this retarded
>OR if i go y+15=-(x^2-6x)
>y+15=-(x^2-6x+9)
>y+24=-(x-3)^2 which is not (3,-6) either

adding 9 in the parenthesis means you're subtracting 9. So subtract 9 from the other side.

Seriously
>being this fucking retarded.

[Anonymous No.7133375]

>>7133368

thank you , i think i got that now

Y+6=-(x-3)^2 right?


but wouldnt
-(x-3)^2 turn into (-x+3)^2 and give me (-3,6)

[Anonymous No.7133377]

Ok, pay careful attention.
y= f(x)= -x^2+6x-15
y +15= -x^2 +6x
-y -15= x^2 -6x
-y -6= x^2 -6x +9
-y -6= (x-3)^2
-y= (x-3)^2 +6
y= -(x-3)^2 -6

from the general form
y= (x-h)^2+k
where the vertex is (h,k)
we find that
h=3
k=-6

there. I've solved it for you.
I recommend you improve your ability to manipulate things algebraically soon. Do not take this lightly, this is simple math. You should be focusing on mastering this and building on it like a foundation.

[Anonymous No.7133378]

>>7133375
-(x-3)^2

in order to bring the negative in side the parenthesis you must take it's square root.
look:
-(x-3)^2
-1 * (x-3)^2
i^2 * (x-3)^2
(xi-3i)^2

so don't do that, it makes things difficult.

I'm sure you're aware of the imaginary number i which is defined as the square root of negative 1

i=-1^(1/2)

make no mistake, just because it is named "imaginary" doesn't make it not real.

[Anonymous No.7133380]

>>7133377
okay i understand that, and really do appreciate it, im working on my math, its harder for me to grasp shit taking an online class, as i cant ask stupid questions like this.... seriously, i appreciate it

the only thing left i dont get is why doesnt the - distribute and make it (-x+3)?

[Anonymous No.7133388]

>>7133378
ohhh fuck okay, fuck. thanks man. gotcha.

the ^2 fucked me i didnt realize that was necessary, okay.

once again thanks for the help , im not sure if it was just you or multiple people, but i appreciate it

[Anonymous No.7133392]

>>7133380
because the term (x-3)^2 is squared
you can't stuff a negative inside a square
see>>7133378

let me also give you a more general way of looking at it.

n^2 = (n)^2 = (-n)^2
-n^2 = -(n)^2 = -(-n)^2

you perform the exponent on ONLY what lies in the parenthesis. THEN the result of that operation is made negative by the negative sign

[Anonymous No.7133398]

>>7133392
fuckin a. alright. Thanks again guys, your help is really appreciated, i get it now. if i could buy you an internet beer, i would

[Anonymous No.7133436]

Way to go boys.

y = -x^2 + 6x - 15
-y = x^2 + 6x - 15
-y - 15 + 9 = x^2 - 6x + 9
-y = (x - 3)^2 + 15 - 9
y = -(x-3)^2 - 15 + 9
y = -1(x - 3)^2 - 6
(3, -6)

[Anonymous No.7133438]

>>7133436
y = -x^2 + 6x - 15
>-y = x^2 - 6x - 15
-y - 15 + 9 = x^2 - 6x + 9
-y = (x - 3)^2 + 15 - 9
y = -(x-3)^2 - 15 + 9
y = -1(x - 3)^2 - 6
(3, -6)
Forgot to change the sign xD