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# Turning point vs symmetry

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Hi friends,

Could someone please explaiin to me whay it is that with a squared function, we have the turning point exactly the same as the axis of symmetry,

however with a cube function, not. Is this because of the inflection point where the concavity changes?...that the maximum and minimum turning points (x-values), are shifted slightly of the axis of symmetry. Because although with a squared function, the turning point is calcuated using

$$x={-b \over2a}$$, the x value can just as easily be calculated by just adding the two adjacent x-intercept values and then devide by 2, but you cannot do this with a cube function?..Thanks for your time...

May 4, 2023

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Hi Jurimagic,

A squared function is always symmetric.   The axis of symmetry (for a concave up or down one is   $$x=\frac{-b}{2a}$$

you can get the roots by adding and minusing   $$\frac{\sqrt{b^2-4ac}}{2a}$$  to the axis of symmetry

Think about the most simple one.  $$y=x^2$$

$$(+x)^2=(-x)^2$$       so it must be symmetricall about y=0

Cubic functions are never symetrical about a line.

eg:  concider y=x^3

$$(+x)^3\ne(-x)^3$$     so it is fefinitelyt not symmetrical about a line,

You need to do lots of work with these and slowly the logic of it all will seep into your brain.

May 4, 2023
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Good morning Melody,

I trust you are well and that things are going great for you.....Thank you for the explanation....You know, I knew there was a reason for that and I kind of understood that the cube function was not symmetrical....I explained it to my student my way, but realised I needed to get a more mathematical approach to explain this, which you did, and I am grateful....Thank you so very much Melody....

You know, I have come to realise that with you and all the other moderators on here, whenever you see a problem, or get some kind of question, the computer kicks in, almost like AI, and basicslly all kinds of approaches are computed, including limitations, with reasons, and a final answer or explanation surfaces within moments.

As for me....well that simply does not happen.......I may think of one thing only...and NOT get the result I want, or the explanation to a question I want....LOL I believe you understand what I'm babbling on about here......

I really take my hat of to you and all the other great people on this forum!!..Thank you

juriemagic  May 5, 2023
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Thanks Juriemagic but getting stuck on the wrong method happens to me quite often too.

Sometimes I can see the answer or at least an approach fairly quickly but that is just from years of exposure and practice.

Also teaching  helps you cement a deeper understanding. Sort of knowing it and muffling your way through may be good enough on a personal level but if you are teaching it effectively you really have to understand it at a deeper, more organised level.  Teaching a topic always made me think about it more.

Melody  May 5, 2023
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Absolutely...as I keep on teaching I'm sure it will also cement into my memory especially with a lot of exposure to the same kind of problematic type of questions....

juriemagic  May 7, 2023
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How it is that you are a teacher teaching math to students, when you can barely comprehend, or not comprehend at all, the elementary math that you teach?

Isn’t this just the blind leading the blind, with you and your students constantly falling into a ditch?

Perhaps you should do your students a favor by going to work for the local nitroglycerin factory, where you can place the “Shake Well Before Using” labels on the bottles.

GA

--. .-

GingerAle  May 7, 2023
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You are such an idiot!!

juriemagic  May 8, 2023