What is a quadratic equation?

A quadratic equation is a second degree polynomial equation. The general form for this kind of equation is: `ax^2 + bx + c = 0`. The constant `a` is called quadratic coefficient and it can’t be zero (otherwise it will be a linear equation). The constant `b` is given the designation of linear coefficient. Finally, the constant `c` is known as constant coefficient or independent term. If the second degree equation doesn’t have the constants `b` or `c`, it is called incomplete quadratic equation, otherwise it will be a complete equation.

Why is this equation so important?

Its graph is a parabola and it describes the movement of a basket ball into the basket. But you may ask: how important is that calculation? Apparently it is of little importance. However, instead of thinking about a basketball ball, if we think about the trajectory of a cannon bullet till it reaches the enemy field, that changes everything. Regarding the last example, it is essential for you to manage to accurately calculate the place where the bullet will cause damage, so as not to waste projectiles or even worse to hit our allies.

And how do you solve that calculation?

The calculation of the place where the bullet hits the ground is done through a study of the zeros of the function, which are also called roots of the equation. To do so we use a formula which will be shown next: `x=(-b +- sqrt(b^2 - 4ac))/(2a)`

What if I do not need to calculate the trajectory of the cannon bullets?

It is often difficult for students to understand the usefulness of what they are learning. One of the most heard questions in the classroom is the following: What is it for? It is a fair question to which lots of teachers don’t unfortunately take trouble to answer. Besides this example the quadratic equation has many other applications in several fields, such as physics, engineering, economics and so on. If we have a look at the roofs of our houses, we will notice that many of them have dish aerials. Those aerials were built based on an important property of these functions that enables the electromagnetic waves collected by the aerial to be reflected to a simple point where the receptor is and that is the focus of the digital aerial.

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