There are various equations we learn and understand in the elementary of high school. Some of those equations are easy, some are complex, and some are plain boring. Whether math is easy for you or difficult, one thing is true – there is no other equation to rival the majestic quadratic equation. I am not just talking about the equation itself but also about the practical implications of the quadratic equation. Let’s be truthful, how many times you have thought that why are you learning this stuff and where it will be useful in the practical world? The answer is almost everywhere. From mobile phone to airplanes, engineers and mathematician are still using the quadratic equation to solve the complex problem.

The story of quadratic equation was started long time ago when the Babylonians introduced the tax system to the farmer. Understandably, the farmers were not happy about the tax so they had to calculate the land needed to be cultivated to make up for the loss in taxes. They came up with the quadratic equation to make up for their loss and estimated the land on which they had to grow crop in order to make the ends meet. As ‘necessity is the mother of invention’, the solution to a simple farming problem is still being used to solve greater problems.

There are hundreds of used of quadratic equation which we observe in the daily life. What we lack is the understanding that this equation can help us estimate the results or simply understand the phenomena. Today, I have compiled a list of practical uses of quadratic equation so the next time you are solving it – you know where it can be used.

### Quadratic Chaos – When Math Meets Biology

The concept of quadratic chaos is defined by the quadratic equation with the focus on biology. Thhe population of a specific species can be estimated accurately with the help of quadratic equation. There is no patter to the growth of species hence it is considered as chaos. In this case x is the population while ‘n’ is the years so xn+1 is considered to be the sub function of xn. If axn was bred successfully while bxn2 dies due to overcrowding – the equation will be,

$$xn + 1 = rxn(1 – xn)$$

The focus of the equation is not just estimating the growth – it is more about understanding and evaluating if the prediction is accurate or hopeless.

### Mobile Phone and Complex Quadratic Equation

The imaginary number were first discovered trying to find an answer to the cubic equation actually. When the imaginary numbers were used to solve the cubic equation, mathematicians were actually able to find the actual results. It was important to justify this mathematical fix otherwise we would have been keep on introducing new letter ultimately running out of letters. Thus the complex umbers were introduced which are the combination of number and alphabets. The incorporation of cubic equation with complex number ultimately led to solve quadratic equation that helped in predicting electron motion. It also assisted in designing the integrated circuit that can perform complex tasks. These circuits are still being used in almost every technological invention including DVDs, computer, cars, and mobile phones. Phone signals convert the speech into high frequency radio waves and this behavior was understood by the quadratic equation. You can say that without the simple quadratic equation ‘x2 = -1’, we would not have invented the mobile phones!

Whether we think about simple machines or the more advanced one – one thing is very clear, it wouldn’t have been possible without calculation. We owe almost all of our invention to mathematics. From growing food as per the need of the population to trying to predict the natural phenomena from observing the movement of galaxies to stepping foot on moon, from calling our loved ones thousand mile away to predict the spread of infection – everything became possible for us when we dived into the realm of mathematics and its branches. One thing is very clear here – if we want to progress further, we need to reintroduce this subject to our student. Making the student understand the concept and logic behind the mathematical equation is the only way forward and we need to focus on it immediately. May be we will get lucky and find next Einstein or Newton!