Functions equations forms

[Oliviera]

Hi,

I'm usually teaching math in French but I'm trying to find an English vocabulary equivalent to "équation de forme canonique" or "équation de forme généralisée".

In French, it's the name of a function written in the form using a, b, h and k parameters.

Like :
f(x) = a(b(x-h))³+k
f(x) = a log_c (b(x-h)) + k
f(x) = a(c)^b(x-h)+k
f(x) = a sin(b(x-h)) + k

etc.

Those equations are all in "canonique" or "généralisée" form.

Is there an equivalent in English?

 

[Steven G]

The h is a horizontal shift, k is a vertical shift and the a is a stretch

 

[Oliviera]

Thank's for your answer Jomo.

I know what the parameters are and what they do. What I would like to know is the name of that form of equations.

For example:

For a quadratic function, f(x)=ax²+bx+c is the "standard form" of equation and f(x)=a(x-h)²+k is the "vertex form".

But what is the name of that last form (the one using a, b, h and k) when applied to other functions, like cubic, exponential, sin, log, etc.?
Is it always "vertex form"?

 

[Dr.Peterson]

We do use words like "canonical", "general", and "standard"; unfortunately, in my experience, such words are not standardized. What one author calls "standard", another might call "general", and each might have another form to which they apply the other term! This depends partly on context and partly on country or culture. To some extent, you just have to state your own terms and definitions.

I am not aware of a standard term for the form you are asking about, which is a transformation of a simple function; I could easily describe it as "transformed" or "transformational" form, but I don't think that is common.

 

[Oliviera]

We do use words like "canonical", "general", and "standard"; unfortunately, in my experience, such words are not standardized. What one author calls "standard", another might call "general", and each might have another form to which they apply the other term! This depends partly on context and partly on country or culture. To some extent, you just have to state your own terms and definitions.

I am not aware of a standard term for the form you are asking about, which is a transformation of a simple function; I could easily describe it as "transformed" or "transformational" form, but I don't think that is common.

Thank you Dr. Peterson,

That's what I thought from what I could find on the Internet. And unfortunately, I don't have access to a lot of math books written in English.

 

[JeffM]

According to ngram, "standard form" has been far more frequent than "canonical form" since approximately 1900. And as a matter of style, I prefer "standard" over "generic" and "generic" over "general." I stongly suspect any of the four will be considered idiomatic by your probable audience.