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...

juriemagic May 4, 2023

#1**+1 **

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.

Melody May 4, 2023

#2**+1 **

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

#3**0 **

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

#4**0 **

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

#5**0 **

**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