Did you know that when a jet or a rocket is launched, the path of the given object is represented with the help of a quadratic equation? The quadratic equations can be calculated in various ways. One of them is the method by using the quadratic formula.
There are various quadratic equations that cannot be easily calculated by factorization. Then, the quadratic formula is used. It is one of the simplest ways which helps to find the roots of a given equation. In this article, we may cover some interesting topics such as: solving quadratic equations, methods related to it, and do a detailed analysis about those topics.
Solving Quadratic Equations
Before knowing about the methods of solving a quadratic equation, one must know about ‘quadratic equations’. The term ‘quadratic’ has been derived from the words Latin which signifies ‘square’. This basically means that the power of the highest variable is the number 2. A quadratic equation is written as ax.x + bx + c = 0 where, a, b and c are considered as the known numbers and ‘x’ is regarded as the unknown number. The process of solving quadratic equations has been classified into various types such as: by the method of factorization, by the graphical representation, by completing squares, and so on. The most easiest and common method of solving a quadratic equation is the process of factoring or factorization. There are other methods as well, but it depends on the question. For Example, if the value of the term ‘b’ is missing from the quadratic equation, a method is used.
Methods of Solving Quadratic Equations
As mentioned above, solving a quadratic equation basically means satisfying an equation by finding the unknown values of the variables. The following points mentioned below signifies the methods of solving a quadratic equation:
- By the process of factoring: The method of factoring is one of the most common and easiest ways to solve a quadratic equation, The steps of implementing the process of factoring is mentioned below:
- The first step is to convert the given equation into the standard form. The equation must be arranged in the form of ax.x + bx + c = 0.
- Then, factorize the given quadratic equation.
- By the property of zero products, you must set the values of factors into zero.
- The last step is to solve the equations you got. The unknown values i.e. ‘x’ can be written in the quadratic equation.
- By the method of Completing Squares: Basically, in this process, the equation is converted into the vertex form from the quadratic form. The step-by-step method is given below which signifies the method of completing squares:
- The first step remains the same in every method of solving a quadratic equation. The equation must be arranged in the form of ax.x + bx + c = 0.
- The second step is to complete the square for the vertex form of the equation.
- Then, solve the equation to get the value of ‘x’ (unknown term).
- By Graphical Representation: The process of solving a quadratic equation by the method of graphical representation requires a coordinate or a bar graph. Then, you must graph or plot the expression (quadratic) in the given bar graph. The following are the steps of graphical representation:
- The first step is to cover the equation into the standard form i.e, ax.x + bx + c = 0.
- The second step is to graph the standard form of the equation in the graph. You can do it either manually or by using the calculator of the graph.
- The last step is to recognize or determine the intercepts of the x-axis. These intercepts are nothing but the roots of the quadratic equation.
Visit Cuemath’s website, if you want to study quadratic equations and formulas in a detailed, interactive and fun manner.