Standard equations

Definitions of STANDARD:

From http://www.merriam-webster.com/dictionary/standard .....

3: something established by authority, custom, or general consent as a model or example : criterion standards;

4: something set up and established by authority as a rule for the measure of quantity, weight, extent, value, or quality

From http://education.yahoo.com/reference/dictionary/entry/standard

Something, such as a practice or a product, that is widely recognized or employed, especially because of its excellence.

From http://dictionary.reference.com/browse/standard

1. something considered by an authority or by general consent as a basis of comparison; an approved model.

2. an object that is regarded as the usual or most common size or form of its kind: We stock the deluxe models as well as the standards.

3. a rule or principle that is used as a basis for judgment: They tried to establish standards for a new philosophical approach.

4. an average or normal requirement, quality, quantity, level, grade, etc.

A Standard is something that should be ... well .... STANDARD!

In Mathematics a Standard equation should be one which all Mathematicians agree is the Standard.  For instance the Standard Equation of a Line is:

Ax + By = C

Where A, B, and C are all integers with no common factor.

And "A" must be positive.

No matter what State or Country, you live in, or which Test you are taking in Middle School, High School, or College, if a teacher asks for the answer to be written in "Standard Form of a Line" a student should know the teacher wants to see "Ax + By = C".

But these days when a teacher asks for "Standard Form of a Quadratic Equation", what does the teacher want exactly?   Doing a Yahoo Search with the words "Standard Form of a Quadratic Equation" yields the following results:

From http://www.analyzemath.com/quadratics/quadratics.htm

Quadratic functions in standard form

f(x) = a(x - h)² + k

From http://www.onemathematicalcat.org/algebra_book/online_problems/write_quad_std_form.htm

A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a does not equal 0.
The form ax^2 + bx + c = 0 is called the standard form of the quadratic equation.

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From http://en.wikipedia.org/wiki/Quadratic_function

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And from the new Texas STAAR Test Algebra II Formula Chart http://www.tea.state.tx.us/student.assessment/staar/math/

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It is that last equation which has this Math Tutor most concerned!  THAT is the equation being used to test our students in Texas on the High Stakes STAAR Test.  And that is NOT the equation which most Math Teachers use to teach students Quadratic Equations and Parabolas.    Of course, we will from now on!    If you will notice the other links above, besides the STAAR Formula, nowhere is there a "4p" mentioned.  Where did this "4p" come from all of a sudden?  And who decided that the equation involving "4p" should be the "Standard" used on the STAAR test?

Yes, I know that  " a = 1/(4p) and that p = 1/(4a) "  but when I learned it we used "c" instead of "p", and "a" was a very important part of the Quadratic Equation.  "a" told you if the graph opened up or down, left or right, and "a" told you how wide or narrow the graph would be.   There is no sign of an "a" in the STAAR Formula Chart version of the Quadratic Equation.   Generations of people have learned how to graph parabolas using "a", including this Math Tutor and most Math Teachers.   Even the dreaded "Quadratic Formula" uses "a" .... with no sign of "p" anywhere.

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Who is messing with the "Standards"? 

Who is setting the "Standards"?  

Here in Lewisville, TX, where we have five different High Schools and at least twenty different Algebra II teachers, I am tutoring students who are learning so many different forms of a Quadratic Equation that their heads are spinning.    As a Math Tutor, MY head is spinning.    I can do all the Math involved and I do understand what the "4p" is and what it is used for.  What I don't understand is why someone is messing with what was once the "Standard"?