Det. x-intrecepts of the reciprocal function: y=1/f(x) and another question

[rich jasper]

So I need help with questions c & d.
And the vertex is (-1, -16), it openng upwards.

[bronze spear]

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[ashen sinew]

Do we have to find the x intercept of f(x) or the reciprocal?

[rich jasper]

f(x) I believe

[ashen sinew]

Ok

[rich jasper]

Or as it says, the parabola.

[ashen sinew]

Yes, it's for f(x) after I read

[rich jasper]

Okie, I was starting to second guess lol

If you respond, ping me. :^)

[ashen sinew]

Ok

@rich jasper at the points x = 3 and x = -6, the graph is going towards 1/0(±∞), then 1/f(x) = 1/0 then f(x) = 0, and that's the x intercept (when y value is equal to zero), x = 3 and x = -6 are the x interceps of f(x)

[rich jasper]

OH Okay that actually makes a lot of sense, I was suspecting (liek I had written it down but wasn't entirley sure.)

Would you be able to help me with the last question?

[rich jasper]

Also may I ask how you got these answers?

It took me a long time to get mine, ugh.

[ashen sinew]

By analyzing the graph

[rich jasper]

No equations, whatsoever?

Just by looking at it, wow

[ashen sinew]

Yea, when you see a graph at positive and negative infinty, it approached 1/0 simple

And the next has some pretty tought equations to solve, one sec

@rich jasper

[rich jasper]

Take ur time, and thank you for explaining c to me.

[ashen sinew]

Np

[rich jasper]

Also this might be a dumb question, but I understand why it's x=3, but why is it x=-6 and not -5?

[ashen sinew]

Oh, yes it's -5, the graph is pixelated

Now it makes sense to me

[rich jasper]

I can post the grpah here in better quality

Yea lemme do just that

[ashen sinew]

No, I drew it and got confused

[rich jasper]

OH okie

[ashen sinew]

@rich jasper are you sure about the vertex? I am wondering

Oh, it's true

[rich jasper]

Sure about it 100%

[ashen sinew]

Yea, 1/(-0,0625) = -16

@rich jasper
Let f(x) = ax^2 + bx + c
Using that the vertex is (-1, -16), c = -16
Then f(x) = ax^2 + bx - 16
Set ax^2 + bx - 16 = 0
Then ax^2 + bx - 16 = a(x - x1)(x-x2)
x^2 + b/a x - 16/a = (x - 3)(x + 5)
x^2 + b/a x - 16/a = x^2 + 5x - 3x -15
b/a = 2 and -16/a = -15
Using -16/a = -15
We get a = 16/15
Then b = 2 × 16/15
b = 32/15
And f(x) = 16/15 x^2 + 32/15 x - 16

Graph it and it's reciprocal a d check if true

[rich jasper]

Lemme do that rn

[ashen sinew]

@rich jasper you're done?

[rich jasper]

I graphed it on desmos, but I'm not sure if I did it right

Im using desmos btw

[ashen sinew]

Graph 1/f(x) if it has the same graph as the question it's true

Check the extermum and the points where it reaches 1/0

@rich jasper ok?

[ashen sinew]

No, the x^2 and x are not in the denominator

[rich jasper]

Okay

[ashen sinew]

Yes

Now wait a sec

[rich jasper]

This one with more points

[ashen sinew]

@rich jasper I found an easier way to proof is:
Let f(x) = ax^2 + bx + c
Set ax^2 + bx + c = 0
The solutions are the x-intercepts x = 3 and x = -5
The vertex is (-1, -16) then c = -16
Using c/a = x1 × x2
a = c/(x1 × x2), a = -16/(3 × -5) a = 16/15
Using -b/a = x1 + x2, b = -a(x1 + x2), b = -16/15 * (3 - 5), b = (-16 * -2)/15, b = 32/15
Then f(x) = 16/15 x^2 + 32/15 x - 16

[rich jasper]

That makes a lot of sense and is easier to understand. Like I can see the logic behind it, wow. Thank you.

[ashen sinew]

No worries

Now, you've finished

[rich jasper]

YES, finallyyy

Now I gotta do more questions. Yay (cri)

[ashen sinew]

Okay

@rich jasper Fun fact: I never studied that in school, but I love math so much that I just skip levels

[rich jasper]

WOW, that is incredibly impressive. Good job!

I used to love math as a kid

Top marks sorta person

[ashen sinew]

I'm still not in high school yet

[rich jasper]

After I went to highschool it-

WOW

MY DUDE

[ashen sinew]

Yea

[rich jasper]

U HAVE TALENT

[ashen sinew]

Ik

[rich jasper]

Good for you, like REALLY GOOD

Keep furthering ur talent for this

[ashen sinew]

I can go and talk abt math with PhD people

I do that always

[rich jasper]

Keep doing that

[ashen sinew]

Yea

[rich jasper]

Keep letting ur mind grow, it can go to many places

[ashen sinew]

Btw, what's your gender? Sorry if you're offended

[rich jasper]

It's alright, no worries

Female btw

[ashen sinew]

I'm a male

[rich jasper]

Well then, hello there person of the opposite gender. 👋

[ashen sinew]

Hi there you too

What's your other questions?

[rich jasper]

OHh no, like Imma do those later

for now its a break

[ashen sinew]

Ok

Dm me if you need me

[rich jasper]

I think it's about logs, but I'm pretty okay with those

[rich jasper]

Will do, thank you once again

[pure dragon]

@rich jasper has given 1 rep to @ebon kraken

[ashen sinew]

Logarithms are pretty simple, bot a big deal

Only integrals, they are the monsters

[rich jasper]

Yeah, and thank goodness for that

oof.... there might be a bit of that, too

I'll actually have to open it up and see

but for now

I nap

[ashen sinew]

Okay

Well, it's 1 am here

[rich jasper]

OH, have I kept u up, crap?? I'm sorry

[ashen sinew]

I'm not going to be available after an hour or two

[rich jasper]

Thats a-okay

[ashen sinew]

No

It's summer break

[rich jasper]

sleep my dude, let ur brain growwwwww

[rich jasper]

Ahh yeah same, but I'm doing summer school to get ahead

[ashen sinew]

Oh

We don't have that here

[rich jasper]

The course I'm doing is advanced functions

[ashen sinew]

Great

My favourite is impossible integrals

Always on them

[rich jasper]

I didn't fail, but I'm assuming that if one were to fail a class, they'd have to retake it the next year?

[ashen sinew]

No, in morocco if you fail you restart the whole year

[rich jasper]

"impossible" integrals, sounds liek my nightmare. But hey, if y like em go get em. :^)

[rich jasper]

WOahh

[ashen sinew]

They are non-elementary functions, monsters

[rich jasper]

Wait, lemme make sense of this. Like say u fail just math, u have to retake the whole year?

[ashen sinew]

No

I failed religious class lol

[rich jasper]

LMFAO

[ashen sinew]

And barely passed history

11.5_20

[rich jasper]

These are classes i'd ace lol

[ashen sinew]

11.5/20 *

[rich jasper]

Ooof

[ashen sinew]

I got a 19.5/20 in math

I wantrd 20/20

[rich jasper]

GOOD JOB, but aim for that .5 next year

If it's okay with u (u dont need to answer) what grade are u in?

[ashen sinew]

I can just go and pass next year now if I want

[rich jasper]

Dude, if I were u I'd do it.

[ashen sinew]

9th, going to high school

[ashen sinew]

Private moroccan schools forbide that

Only public

And next year is my public year

Bc no private school has a math class

[rich jasper]

I'm going to 12th, and then off to uni for comp sci, i'm hoping.

[ashen sinew]

Here, private schools are like public ones in usa but worse

And public ones here are heaven

[rich jasper]

Oh so, say u do really well in those years, u'd be able to skip.

[ashen sinew]

Yep

[rich jasper]

That's funny imo, like the complete opposite.

[ashen sinew]

You talk to the teacher, principal and counselor. They inform the academy and you take a finale test

[rich jasper]

Take it. Cause I assume ur gonna go do a post-secondary like uni, right?

The more years u have, the younger u'll get outta uni and it's impressive to companies.

[ashen sinew]

I think I'll just go for PhD from now

Idk, I can prepare myself

[rich jasper]

Ooh, thinking big. PhD for math?

[ashen sinew]

Yea

[rich jasper]

Very good plan.

Ay man, ur actually gonna ace it.

[ashen sinew]

Imagine this, I studied and tamed integrals and then discovered derivatives

[rich jasper]

I'm doing something sorta similar, making myself relearn how to code so I can improve.

[ashen sinew]

Coding is my hobby

[rich jasper]

To me that sounds PAINFUL, but frick yeah, that is amazing.

[ashen sinew]

I never knew WHY +C

[rich jasper]

I'd say it was my hobby, but I've been so busy I haven't done it in half a year, oof

[ashen sinew]

I always try to code

[rich jasper]

Oh and about coding, I assume ur self taught?

[ashen sinew]

Python, I'm a master

Kinda

Not really

[rich jasper]

The way I view it, it really is like a language. U need to keep doing it or u will forget

[ashen sinew]

Yea

Why so many messages?

[rich jasper]

Ugh, haven't touched phyton (oh and my school has it as a course.) I knew Html 4 and 5, and Java (although I hate it)

[ashen sinew]

We started chatting

[rich jasper]

hello

[ashen sinew]

Yeah I seee

Lol

I only know python lmao

[rich jasper]

I did some phyton, and imo it's the easier version of java

Java, JAVA SUCKS

[ashen sinew]

@rich jasper Dm me and close this, ok?

[rich jasper]

So long-winded

[ashen sinew]

And JAVA SUCKS

[rich jasper]

Sure.

[ashen sinew]

JAVA SUCKS

JAVA SUCKS