The Quadratic Equation

The matriculation exams are slowly coming to an end. It is hoped that the majority have successfully overcome the obstacles and will be able to enter life with a capital letter or continue their studies at a higher education institution. But it is certain that it is a huge relief to get over it and get rid of the stress package of school with exams and answers. To what extent the “graduation” exam contributes to actual graduation, I could only observe with considerable doubt even at my own graduation, but this feeling only increased during my children’s studies. One of my favorites from the course material is the solution formula for the quadratic equation, which everyone had to know when they woke up from their sleep. In the German-speaking area, it is also called “Mitternachtsfomel”, i.e. the midnight formula. The formula says that if a quadratic equation says that

ax²+bx+c=0,

then the maximum two x values representing the solution can be calculated using the following formula:

For some reason, the school system is in love with this formula.

If I think about it very honestly, I have lived a career of well over 25 years as a development engineer at some pretty well-known companies, but I can say with certainty that I hardly had to use the above formula, or if I had to, it would have been enough to know that it existed and that it was possible to find on the Internet (at the beginning of my professional career, we preferred to read books in such cases, because the Internet required a telephone modem and was slow).

I suspect that the school system likes this formula because it is just such a large curriculum that can easily be assessed in one package – as if assessment is the most important goal of education.

It also crossed my mind that today’s education system looks back on long traditions (so it sounds better than if I say it’s an old fossil), and as part of war preparation, the trajectory of cannonballs can be approximated with a quadratic equation, which is vital in a war of the last century volt. But a few years have passed since then. A hundred years ago, if a student learned a trade well, he could pass it on to two more generations, the basics were still largely valid. Today, in the age of digitization and artificial intelligence, by the time a student completes a 4-year school, new professions come into vogue and, for example, a ChatGPT comes into play, which can make the meaning of written homework at home questionable, not to mention the fact that you learned a profession in a couple of years it is devalued by technical progress during graduation. I think this formula should not be forced so much, just mention that there is such a thing and that’s it. In the time freed up in this way, a number of useful study materials could be included, for example, help to deal with stress, more conscious awareness of one’s own emotional reactions. In general, school should not teach curriculum, but develop skills. As for the quadratic equation, yes, it is worth getting to know its properties (for example, we had a spring parabola that goes up like a tulip, and an autumn parabola that goes down).

As for the solution formula, I recommend the program DockCalc, which simply calculates the solutions. Such a calculation is shown in the following example:

You can download the DockCalc program here, and it will come in handy in countless other calculations. Have fun with the software!