I need help with this | Mathematics | Page 1

dusky hedge Dec 17, 2024, 1:09 AM

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ancient jasperBOT Dec 17, 2024, 1:09 AM

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dusky hedge

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buoyant scarab Dec 17, 2024, 1:12 AM

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dusky hedge

what's the entire question?

dusky hedge Dec 17, 2024, 1:14 AM

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I just need to know why the vertex is 2,0

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buoyant scarab Dec 17, 2024, 1:15 AM

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ok, our equation is $-5x^2+20x$

turbid flumeBOT Dec 17, 2024, 1:15 AM

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Ravioli ≥ ^• ∧ •^ ≤

dusky hedge Dec 17, 2024, 1:15 AM

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Yeah

buoyant scarab Dec 17, 2024, 1:16 AM

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This can be written as $-5x(x-4)$

turbid flumeBOT Dec 17, 2024, 1:16 AM

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Ravioli ≥ ^• ∧ •^ ≤

buoyant scarab Dec 17, 2024, 1:16 AM

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So, our quadratic has roots at x=0 and x=4

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Hence, its vertex will appear at the midpoint of the roots

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which is x=2

dusky hedge Dec 17, 2024, 1:16 AM

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What

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Where did we get 4 and 0 from

buoyant scarab Dec 17, 2024, 1:17 AM

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turbid flume **Ravioli ≥ ^• ∧ •^ ≤**

-5x(x-4) = 0

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When is the left equal to 0?

dusky hedge Dec 17, 2024, 1:18 AM

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Uhm

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When it’s less than or greater than

buoyant scarab Dec 17, 2024, 1:19 AM

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We want values of x such that -5x(x-4) is equal to 0

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Notice that it can be split into 2 factors, namely
-5x and (x-4)

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When either of these is equal to 0, the entirety of -5x(x-4) will be equal to 0, as multiplying any number by 0 will give you a 0

dusky hedge Dec 17, 2024, 1:20 AM

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Wait so I can’t just put this into like a plotting website

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And give it the max value

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That’s what I’ve been doing

buoyant scarab Dec 17, 2024, 1:21 AM

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Well, that would work, yes
But as you've made a help post, I'm assuming that you actually want to understand the topic, or is that not the case?

dusky hedge Dec 17, 2024, 1:21 AM

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Oh well

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In class I’ve just been using this thing called Desmond

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*desmos

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And I’m allowed to use it on any test or exam

buoyant scarab Dec 17, 2024, 1:22 AM

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Oh

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then you're good lmfao

dusky hedge Dec 17, 2024, 1:22 AM

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So I want to make sure I get other things that I’m confused about

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But I don’t understand why

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The vertex is 2

buoyant scarab Dec 17, 2024, 1:23 AM

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it's because at x=0 and x=4, -5x^2 + 20x = 0
And the vertex always appears at the point in the exact middle of the roots

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For the second line, you'll just have to take it for granted- I'm not the best math teacher

dusky hedge Dec 17, 2024, 1:24 AM

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But Luke

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*like

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When I put it into this desmos app thing

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It gave me this

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buoyant scarab Dec 17, 2024, 1:24 AM

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It should return your vertex point as (2,20)

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Yep, exactly that

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In your solution, you wrote the vertex as (20,2)

silver edge Dec 17, 2024, 1:25 AM

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an alternative method would be to complete the square, a standard method of obtaining the vertex

buoyant scarab Dec 17, 2024, 1:25 AM

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silver edge an alternative method would be to complete the square, a standard method of obta...

or that 😭

dusky hedge Dec 17, 2024, 1:25 AM

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Oh

buoyant scarab Dec 17, 2024, 1:25 AM

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That also works 😭

dusky hedge Dec 17, 2024, 1:26 AM

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Wait like the box method

buoyant scarab Dec 17, 2024, 1:26 AM

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what

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Um, do you know what completing the square means?

dusky hedge Dec 17, 2024, 1:26 AM

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Like

buoyant scarab Dec 17, 2024, 1:26 AM

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?

dusky hedge Dec 17, 2024, 1:27 AM

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This stuff

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buoyant scarab Dec 17, 2024, 1:27 AM

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Can you demonstrate it once?

dusky hedge Dec 17, 2024, 1:27 AM

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buoyant scarab Dec 17, 2024, 1:28 AM

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ok, and how does that help you work towards a solution?

dusky hedge Dec 17, 2024, 1:28 AM

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Like this stuff

dusky hedge Dec 17, 2024, 1:28 AM

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buoyant scarab ok, and how does that help you work towards a solution?

I don’t know I just thought this is what you were talking about

buoyant scarab Dec 17, 2024, 1:28 AM

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dusky hedge I don’t know I just thought this is what you were talking about

This isn't what I'm talking about lol

dusky hedge Dec 17, 2024, 1:28 AM

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Or is it like the x axis is the vertex

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Bc some guy told me that before

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But he said

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Axis of symmetry

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Is the x value of the vertex

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So idk what this is

buoyant scarab Dec 17, 2024, 1:29 AM

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The vertex lies on the axis of symmetry

dusky hedge Dec 17, 2024, 1:29 AM

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What

silver edge Dec 17, 2024, 1:29 AM

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i mean, doing it using the midpoint would be the best approach

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so just continue on with that

dusky hedge Dec 17, 2024, 1:29 AM

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How do I do that

silver edge Dec 17, 2024, 1:29 AM

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didn't they already show you how?

dusky hedge Dec 17, 2024, 1:29 AM

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buoyant scarab Dec 17, 2024, 1:29 AM

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silver edge i mean, doing it using the midpoint would be the best approach

ik, but do yk a way to intutively show why it's at the midpoint without calc?

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And without completing the square, unfortunately

dusky hedge Dec 17, 2024, 1:30 AM

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I’m in Algebra 1

silver edge Dec 17, 2024, 1:30 AM

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buoyant scarab ik, but do yk a way to intutively show why it's at the midpoint without calc?

with the roots of the equation?

buoyant scarab Dec 17, 2024, 1:30 AM

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silver edge with the roots of the equation?

yeah- 😭

silver edge Dec 17, 2024, 1:30 AM

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yeah that's really it then

buoyant scarab Dec 17, 2024, 1:30 AM

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The only proofs I can think of require knowing how to complete the square or Calc

dusky hedge Dec 17, 2024, 1:30 AM

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😀 ❓

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I hate math

silver edge Dec 17, 2024, 1:30 AM

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silver edge with the roots of the equation?

because x^2 is symmetric about the y axis

buoyant scarab Dec 17, 2024, 1:31 AM

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Ok Jung, do yk the identity $(a+b)^2=a^2+2ab+b^2$ and the analogous result for $(a-b)^2$

turbid flumeBOT Dec 17, 2024, 1:31 AM

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Ravioli ≥ ^• ∧ •^ ≤

buoyant scarab Dec 17, 2024, 1:31 AM

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?

dusky hedge Dec 17, 2024, 1:31 AM

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What 😄

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Do I have to solve it?

buoyant scarab Dec 17, 2024, 1:31 AM

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dusky hedge What 😄

That's an algebraic identity

dusky hedge Dec 17, 2024, 1:31 AM

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What does A= and what does B=

dusky hedge Dec 17, 2024, 1:32 AM

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buoyant scarab That's an algebraic identity

Erm

silver edge Dec 17, 2024, 1:32 AM

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the coefficients of the equation

buoyant scarab Dec 17, 2024, 1:32 AM

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they can be anything you want

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(numbers ofc)

dusky hedge Dec 17, 2024, 1:32 AM

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Ig I know how to do that

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Isn’t it just addition and multiplication and all that

silver edge Dec 17, 2024, 1:32 AM

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wdym by that

buoyant scarab Dec 17, 2024, 1:32 AM

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Yeah basically

dusky hedge Dec 17, 2024, 1:32 AM

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Since A and B can be anything I want?

buoyant scarab Dec 17, 2024, 1:33 AM

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Try simplifying (a+b)(a+b)

dusky hedge Dec 17, 2024, 1:33 AM

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What does this have to do wirh rhe vertex

dusky hedge Dec 17, 2024, 1:33 AM

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buoyant scarab Try simplifying (a+b)(a+b)

Uhm

buoyant scarab Dec 17, 2024, 1:33 AM

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dusky hedge What does this have to do wirh rhe vertex

You'll see

dusky hedge Dec 17, 2024, 1:33 AM

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With what numbers

silver edge Dec 17, 2024, 1:33 AM

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they are showing you how to complete the square

dusky hedge Dec 17, 2024, 1:33 AM

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Like 0,4

buoyant scarab Dec 17, 2024, 1:33 AM

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dusky hedge With what numbers

No numbers

dusky hedge Dec 17, 2024, 1:33 AM

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Then what am I suppose to do

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Oh

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Erm

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So is it

buoyant scarab Dec 17, 2024, 1:33 AM

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You know how to deal with variables, I hope?

dusky hedge Dec 17, 2024, 1:34 AM

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A^2 and B^2

buoyant scarab Dec 17, 2024, 1:34 AM

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silver edge they are showing you how to complete the square

(Also it's he lmfao)

buoyant scarab Dec 17, 2024, 1:34 AM

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dusky hedge A^2 and B^2

no...

dusky hedge Dec 17, 2024, 1:34 AM

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A2 and B2

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I’m failing this final omg

buoyant scarab Dec 17, 2024, 1:34 AM

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(a+b)^2 = (a+b)(a+b) = a(a+b) + b(a+b) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2

dusky hedge Dec 17, 2024, 1:35 AM

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😄?

buoyant scarab Dec 17, 2024, 1:35 AM

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That was what I was looking for

dusky hedge Dec 17, 2024, 1:35 AM

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What is that even for

buoyant scarab Dec 17, 2024, 1:35 AM

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For completing the square, which is the simplest way I can think of for teaching you why the vertex is appearing at 2, or more abstractly, at the midpoint of the roots

dusky hedge Dec 17, 2024, 1:36 AM

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This is so confusing what the heck

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I never learned this

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Idk what this is

buoyant scarab Dec 17, 2024, 1:36 AM

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hmm

dusky hedge Dec 17, 2024, 1:36 AM

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I just plot it in desmos

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And take the highest or lowest point

buoyant scarab Dec 17, 2024, 1:37 AM

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Ok, suppose I have the equation (x-3)(x-1) and I want to write it in vertex form

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First, I'll expand the entire thing

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x^2 - 4x + 3

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Then,

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x^2 - 4x + 4 - 4 + 3
Can you see what I did here?

dusky hedge Dec 17, 2024, 1:38 AM

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buoyant scarab Dec 17, 2024, 1:38 AM

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Yeah, there's vertex form

dusky hedge Dec 17, 2024, 1:38 AM

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Yeah

buoyant scarab Dec 17, 2024, 1:38 AM

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That's what you want here

dusky hedge Dec 17, 2024, 1:38 AM

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Ok

buoyant scarab Dec 17, 2024, 1:39 AM

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so,
(x^2 - 4x + 4) - 4 + 3

dusky hedge Dec 17, 2024, 1:39 AM

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What

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😭

buoyant scarab Dec 17, 2024, 1:39 AM

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We're writing (x-3)(x-1) in vertex form

dusky hedge Dec 17, 2024, 1:39 AM

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So the vertex is

buoyant scarab Dec 17, 2024, 1:39 AM

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buoyant scarab Ok, suppose I have the equation (x-3)(x-1) and I want to write it in vertex form

read from here

dusky hedge Dec 17, 2024, 1:39 AM

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3,0 and 1,0

buoyant scarab Dec 17, 2024, 1:39 AM

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dusky hedge 3,0 and 1,0

no, those are the roots

dusky hedge Dec 17, 2024, 1:40 AM

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So where do we get these numbers from

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Oh the two vertex points?

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So in this case 2,20?

buoyant scarab Dec 17, 2024, 1:40 AM

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We're just working through an example just in case you've been taught this before and just need your memory jogged

dusky hedge Dec 17, 2024, 1:41 AM

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dusky hedge Oh the two vertex points?

So is this it?

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Or no?

buoyant scarab Dec 17, 2024, 1:41 AM

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dusky hedge So in this case 2,20?

No, we're doing a different example rn

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Completing the square should be taught in an Algebra I class I think

dusky hedge Dec 17, 2024, 1:41 AM

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But like if we were correlating it to this problem would those be the points

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So I can understand it better

dusky hedge Dec 17, 2024, 1:42 AM

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buoyant scarab Completing the square should be taught in an Algebra I class I think

Well I didnt finish algebra 1 yet

buoyant scarab Dec 17, 2024, 1:42 AM

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dusky hedge But like if we were correlating it to this problem would those be the points

Well, the vertex would occur at (2,h) for some h

dusky hedge Dec 17, 2024, 1:42 AM

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What’s H

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Input?

buoyant scarab Dec 17, 2024, 1:42 AM

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dusky hedge Well I didnt finish algebra 1 yet

It should have been taught to you by now I think? I'm not sure though, the way I learnt math is cursed

buoyant scarab Dec 17, 2024, 1:42 AM

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dusky hedge Input?

h is just a variable whose value we wis-

dusky hedge Dec 17, 2024, 1:42 AM

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I don’t know what I’m doing 😭

buoyant scarab Dec 17, 2024, 1:43 AM

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When are your exams?

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I can tell you a shortcut for the answer if you wish using desmos

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but if you want to understand why the vertex occurs at 2 for your problem, that will require a bit of work

dusky hedge Dec 17, 2024, 1:44 AM

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I have my math final on Thursday I’m so done

dusky hedge Dec 17, 2024, 1:45 AM

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buoyant scarab but if you want to understand why the vertex occurs at 2 for your problem, that ...

Well I thought it was 2,20

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Bc that’s what I did on the first page of this packet

buoyant scarab Dec 17, 2024, 1:45 AM

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dusky hedge Well I thought it was 2,20

it is

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what

dusky hedge Dec 17, 2024, 1:45 AM

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It says the answers 2

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On my packet

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On the answer sheet

buoyant scarab Dec 17, 2024, 1:45 AM

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Ah- you probably misread the problem

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They're probably asking where the vertex occurs

dusky hedge Dec 17, 2024, 1:45 AM

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It said find the maximum height

buoyant scarab Dec 17, 2024, 1:46 AM

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huh

dusky hedge Dec 17, 2024, 1:46 AM

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Ignore the thing at the bottom

buoyant scarab Dec 17, 2024, 1:46 AM

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The maximum height of the water spray should be 20

dusky hedge Dec 17, 2024, 1:46 AM

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That’s the answer key

dusky hedge Dec 17, 2024, 1:46 AM

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buoyant scarab The maximum height of the water spray should be 20

So why is it 2

odd valley Dec 17, 2024, 1:47 AM

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Probably a typo

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They typed in the x coordinate instead of the y coordinate

dusky hedge Dec 17, 2024, 1:47 AM

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This other guy said the same thing for like two other problems

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But like idk

buoyant scarab Dec 17, 2024, 1:47 AM

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odd valley Probably a typo

They've given the answers for the points that should be marked on the graph lol

dusky hedge Dec 17, 2024, 1:47 AM

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I’m not trying to mess up this math and then fail my exam

buoyant scarab Dec 17, 2024, 1:48 AM

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They haven't given the answers for the actual question 😭

dusky hedge Dec 17, 2024, 1:48 AM

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It says graph answers:

buoyant scarab Dec 17, 2024, 1:48 AM

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Yep, those are the points which you were supposed to mark on the graph, and you did so

dusky hedge Dec 17, 2024, 1:48 AM

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Like this is mine

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And the other one is the answers

buoyant scarab Dec 17, 2024, 1:49 AM

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There's only one mistake in yours, the vertex point should be (2,20) not (20,2)

dusky hedge Dec 17, 2024, 1:49 AM

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Oh

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I guess this study guide answer sheet is all wrong then

buoyant scarab Dec 17, 2024, 1:50 AM

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You'll pass lmfao

dusky hedge Dec 17, 2024, 1:50 AM

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Bc this is like the 4th wrong one

odd valley Dec 17, 2024, 1:50 AM

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Study guide maker was probably drunk when bro made this

buoyant scarab Dec 17, 2024, 1:50 AM

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dusky hedge I guess this study guide answer sheet is all wrong then

Actually, the organization of the study guide is all wrong lmfaooo
You're doing everything correct

dusky hedge Dec 17, 2024, 1:50 AM

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😭

buoyant scarab Dec 17, 2024, 1:50 AM

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odd valley Study guide maker was probably drunk when bro made this

Agreed

dusky hedge Dec 17, 2024, 1:50 AM

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buoyant scarab Actually, the organization of the study guide is all wrong lmfaooo You're doing ...

This teacher I swear

buoyant scarab Dec 17, 2024, 1:51 AM

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Vro probably confused the vodka with water

dusky hedge Dec 17, 2024, 1:51 AM

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😭

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Wait I need help wirh smth else

buoyant scarab Dec 17, 2024, 1:51 AM

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Algebra I teachers pretty much don't care
Higher math classes are more fun though

buoyant scarab Dec 17, 2024, 1:51 AM

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dusky hedge Wait I need help wirh smth else

Oh-

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I'm going to leave soon

dusky hedge Dec 17, 2024, 1:52 AM

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Ok

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😭

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I’ll google it dw

buoyant scarab Dec 17, 2024, 1:52 AM

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send it anyways

dusky hedge Dec 17, 2024, 1:52 AM

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😐

buoyant scarab Dec 17, 2024, 1:53 AM

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ah yes, they simply wish to torture you

dusky hedge Dec 17, 2024, 1:53 AM

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😢

buoyant scarab Dec 17, 2024, 1:53 AM

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SHove the function into desmos and check where it intersects the x-axis

dusky hedge Dec 17, 2024, 1:54 AM

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I got one part

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buoyant scarab Dec 17, 2024, 1:54 AM

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buoyant scarab SHove the function into desmos and check where it intersects the x-axis

do this for the first part

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and third part

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and fourth part

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wow

dusky hedge Dec 17, 2024, 1:55 AM

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buoyant scarab Dec 17, 2024, 1:55 AM

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uhhh
-3x^2 + 24x + 27

dusky hedge Dec 17, 2024, 1:55 AM

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Also the vertex is -4,-21 so like??

buoyant scarab Dec 17, 2024, 1:55 AM

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I think you typed it in wrong 😭

dusky hedge Dec 17, 2024, 1:55 AM

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Oh

buoyant scarab Dec 17, 2024, 1:55 AM

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It should be opening downwards

dusky hedge Dec 17, 2024, 1:55 AM

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Whoops

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Nvm got it

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#

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Got more

buoyant scarab Dec 17, 2024, 1:57 AM

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ok so your quadratic is in the form of A(x+1)(x-9) for some number A
it's vertex is at (4,75)
Hence the maximum value is 75000

dusky hedge Dec 17, 2024, 1:57 AM

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75=75000??

buoyant scarab Dec 17, 2024, 1:57 AM

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Yeah, the function is returning the profit in THOUSANDS of dollars lmfaooo

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very important word right there

dusky hedge Dec 17, 2024, 1:58 AM

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I see I see 🤔

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So X is dollars

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So Y is boxes?

buoyant scarab Dec 17, 2024, 1:59 AM

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opposite

dusky hedge Dec 17, 2024, 1:59 AM

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Why

buoyant scarab Dec 17, 2024, 1:59 AM

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x is boxes, y is dollars, it's in the question

dusky hedge Dec 17, 2024, 1:59 AM

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Why

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It says

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X dollars

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And function = y right??

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F(x)= function = y

buoyant scarab Dec 17, 2024, 2:00 AM

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Can you send a photo of the entire question?

dusky hedge Dec 17, 2024, 2:00 AM

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buoyant scarab Dec 17, 2024, 2:01 AM

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Oh you're right

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Sorry

dusky hedge Dec 17, 2024, 2:01 AM

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Oh ok

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I was scared for a sec 😭

buoyant scarab Dec 17, 2024, 2:02 AM

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You'llbe fine

dusky hedge Dec 17, 2024, 2:02 AM

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Nah my grades a 77 rn

buoyant scarab Dec 17, 2024, 2:02 AM

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C

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You'll be fine

dusky hedge Dec 17, 2024, 2:02 AM

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This exam is my last hope

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I need a B

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So I must get an 100

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😍

#I need help with this