Quadratic Equations in Two Variables

The quadratic equation is used in order to express a certain equation in such a manner that the x has two different values. Based on the negative and positive roots of the equations, the solutions of the quadratic equation have been found in the algebraic expression. Following that fact of mathematics, the current study has intended to represent the discussion based on the quadratic equations in two variables. The study will include a discussion based on solving the problems related to the quadratic equations.

Explanation of Quadratic Equations

The equations in the algebraic expression consist of the second degree of x is determined as the quadratic equation. It has been seen that the word quadratic is derived from the word quad. This particular word means the square value.  The first condition of representing the quadratic equation is to make the coefficient non-equivalent to the value that denotes zero. Based on this particular scenario, in order to represent the equation, the value of the x2 has been written earlier than positioning other values in the equation. 

Quadratic Equations in Two Variables

As per the rules of algebra, it has been seen that in the case of the representation of a quadratic equation in two variables, the equation is represented as ax2 + bxy + cy2 + dx + ey + f = 0. Here, in this particular equation, as combining two variables, the values of the c, a, b, e and f are conjectures as an arbitrary constant. The shape of the curve has been decided by two aspects of the equation : the discriminant and the invariant. 

Factors of Solving Quadratic Equations

Generally, a quadratic equation can be written in the form of ax 2 + bx + c = 0 where the value of a is considered the equivalent to zero. Based on these equations, several factors are used for finding the solution of the quadratic equation that is mentioned below:

• By pulling all the terms on any one side of the equal sign
• By setting each factor equal to zero
• By solving each of the separate equations one can possibly get

Examples of Different Forms of Quadratic Equation 

The quadratic equation can be classified into three different forms that include the forms like standard form, vertex form and the factored form. In such cases where the equations and the formulas are represented with the highest degree first, the standard form of the quadratic equation is formed, that is y=ax2+bx+c. On the contrary, by doing the factor of the standard equation formula, one can get the factored form that is y=a(x−r1 )(x−r2 ). On the other hand, to represent the lowest form of the vertex form has been represented as y= a(x−h)2+k

Definition of Quadratic Equation Formula 

In order to have the value of the root of a quadratic equation, using the quadratic formula is the simplest way. On the other hand, it can be stated that some equations exist that cannot be factorised in a certain manner in an easy way. In such scenarios, the quadratic equation formula has been used in the most convenient manner. It has been seen that the value of two roots has been expressed as a singular expression in the equation that is [-b ± √(b² – 4ac)]/2a.

Ways of Graphing A Quadratic Expression

The graphing of the quadratic expression can be expressed as a quadratic function as per the way that denotes the equation that is y = ax2 + bx + c. in order to obtain the subsidiary values for the x, the value of y can be used in order to solve the quadratic equation. These values or points can be represented on the axis that is coordinating in order to obtain a parabola shape in the quadratic expression.  

Conclusion 

Based on the discussion section of this current study, it can be stated that this study has focussed on representing the quadratic equation in two variables. It has been found in the discussion section that the two variables of the quadratic equation can be x and y. The values of these two variables of the equation can be determined by the discriminant. On the other hand, the study further included information regarding the ways of graphing a quadratic expression as well as displaying in-depth knowledge.