Functions equations forms

Oliviera

New member
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 logc (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?

Jomo

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

Oliviera

New member

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

Elite Member
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

Oliviera

New member
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

Elite Member
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.

Last edited: