#Quadratic Curves, Origin Shifting

132 messages · Page 1 of 1 (latest)

glacial ploverBOT
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dusty peak
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No need for the caps 💀

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Could you elaborate?

burnt steppe
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yes

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so

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i have a quadratic

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say symmetric about

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x = a

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right

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lets call that curve f(x)

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the curve for f(x-4) should be symmetric about x = a+4 right

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and the curve for f(-x) should be symmetric about x = -a

topaz copper
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You shifted origin at 4,0 then

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,w plot (x-a)^2

long sundialBOT
burnt steppe
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wtf is this 😭

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3d streched paraboa

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anyways

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PLS LISTEN TO THE ACTUAL DOUBTT PLS

burnt steppe
topaz copper
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Mb

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Wait

burnt steppe
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oki

topaz copper
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,w plot (x-4)^2

long sundialBOT
burnt steppe
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yeah thats what i said

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shifting the whole curve 4 units right

topaz copper
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Yes

burnt steppe
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and

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f(-x) means

topaz copper
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What's the problem

burnt steppe
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inverting the whole curve about the y axis

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right

topaz copper
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?

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What's f(x)

burnt steppe
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a quadratic

still pollen
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You got both right

burnt steppe
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me?

still pollen
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Yeah

topaz copper
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If f(x) = x^2

burnt steppe
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okay so

topaz copper
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F(-x) is same

still pollen
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the a+4 and -a things

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What’s your doubt?

burnt steppe
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okay so

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the thing is

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if i take

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f(2-x)

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im supposed to

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flipp the curve about y axis

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and then

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take it back 2 units

topaz copper
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No

burnt steppe
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so it should be

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symmetrical about -a-2 right

topaz copper
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Give me f(x) properly first

burnt steppe
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its a quadratic

still pollen
topaz copper
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ax^2 + bx + c?

burnt steppe
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whyy

burnt steppe
burnt steppe
topaz copper
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For -x it would be ax^2 - bx + c

topaz copper
burnt steppe
topaz copper
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Not really

burnt steppe
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i can replace x with -x and write the eqn myself too but im talking in graph rn

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what changes in the graph when i make those changes to the input

topaz copper
still pollen
burnt steppe
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obviously it would

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its okay if youre not familiar with curve transformation

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please atleast dont confuse me 😭

topaz copper
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How is this flipping 😭

burnt steppe
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how is this not?

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mirrored about y axis

topaz copper
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X cordni Vertex will change sign

burnt steppe
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and what is that calleD?

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MIRRORING ABOUT Y AXIS

still pollen
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f(a + h) = f(a - h) for any h.
Let g(x) = f(2 - x)
g(b + t) = g(b - t) for some t, where b is the axis of symmetry
f(2 - (b + t)) = f(2 - (b - t))
f((2 - b) - t) = f((2 - b) + t)
When 2 - b = a so
b = 2 - a,
and so its symmetrical around x = 2-a

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@burnt steppe

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Sorry it took a while

burnt steppe
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whats is the

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reason for

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first eqn

still pollen
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Because a is the axis of symmetry

topaz copper
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@burnt steppe the whole graph isn't flipping only the x cord of vertex 😢

burnt steppe
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oh

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yess

burnt steppe
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but

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during an exam

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i dont wanna go all over this procedure

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how do i figure this out

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just through looking at the input

still pollen
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You want a formula of some sort?

burnt steppe
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no no

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like

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when i look at f(x-4)

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i know

topaz copper
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@still pollen trust me you are making this complex

burnt steppe
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that its just shifted 4 units ahead

topaz copper
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@burnt steppe what's the vertex of a quadratic ax² + bx + c

burnt steppe
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and its -b/2a

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, - d/4a

topaz copper
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Yes so d depends on b²

burnt steppe
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andd??

topaz copper
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X cord depends on b

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F(-x) sign of b will flip

burnt steppe
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every function in this universe will flip when x is replaced with -x

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not just this quadratic

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soo yeah...

topaz copper
burnt steppe
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and?

topaz copper
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So x coordinate will change signs

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It's symmetrical abt -a

burnt steppe
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when did i deny that its not?

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ive been saying the same exact thing that the graph is mirrored about y axis

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which inherently means the axis of symmetry is also mirrored

topaz copper
burnt steppe
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it is

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you can try replacing x with -x on desmos

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on ANY function

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ANYYY function

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and see for yourself

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is that alright?

topaz copper
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Yeah you are right mb