Maximum and Minimum Value of Quadratic Equation

In accordance with the terminology of algebra, the expression of the second-degree algebraic equation is represented by the quadratic equation. In algebra, various scenarios can be found where the quadratic equation has been used as a solution. In a quadratic equation, the X has two kinds of values. These two kinds of values of X are called the roots of the quadratic equation. Based on these facts, the current study has intended to determine the maximum and minimum values of the quadratic equation. 

Quadratic Equation: Overview

The standard form of the quadratic equation is ax2+bx+c= 0. In this equation, it has been conjectured that the a and b are the coefficients and the x is the variable. On the other hand, the c has acted as a constant term in the equation. As per these conditions, the first scenario will be a quadratic equation that represents the coefficients of x2 is a term that is not equal to 0. In order to write the quadratic equation in a standard manner, the term x2 needs to be written first followed by the term x. In the final stage, the constant term needs to be written. 

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The Formula of a Quadratic Equation 

The quadratic formula is generally used in order to find the root of the equation that is considered quadratic. There are some cases or certain equations found in algebra that cannot be factorised in an easy manner. In such scenarios, the quadratic formula has been used in order to find the root in the most possible ways. Two roots of the equation that are quadratic can be represented as a singular expression. The signs, positive and negative can be used in an alternative manner for obtaining the two distinct roots of the quadratic equation = [-b ± √(b² – 4ac)]/2a

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Method to Solve Quadratic Equation 

In order to find the solution to a quadratic equation, the four methods can be applied that are mentioned in the below section:

• The quadratic equation can be factorised
• In order to find the roots, the formula method can be applied
• The method regarding the completing of the square can be applied as well
• For finding the roots, the graphing method can be used

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Determining the Maximum Value of the Quadratic Equation 

Among the three distinct methods of finding the maximum value of an equation that is quadratic, the graphing method can be a beneficial one. The primary benefit one will have is that the person will be able to find the root by graphing the equation in a visual manner by locating the maximum point on the graph. For instance, it can be stated that if the equation has been represented in the form of ax2 +bx+c, the formula for finding the maximum value will be max= c- (b2/4a).

Determining the Minimum Value of the Quadratic Equation

Using a graph, the minimum value of an equation that is quadratic can be found in an easy way. In order to find the minimum value in a visible manner, one can use the graph in order to point out the minimum point of the quadratic equation. In case one has the equation that is represented in a way like y= ax2+bx+c, one will be able to find the minimum value of the quadratic equation by following the equation of having a minimum value that is min= c- b2/4a. 

Factorization of Quadratic Equation

A specific equation of steps is needed to be followed in order to attain the factorization of the equation that is quadratic. For getting a general form of the factorization of the quadratic equation, that is ax2 +bx +c=0, the equation is represented in the below section:

x2 + (a + b)x + ab = 0

x2 + ax + bx + ab = 0

x(x + a) + b(x + a)

(x + a)(x + b) = 0

Based on this explanation of the factorization, an example can be solved that is x2 + 5x + 6 = 0 where the values will be (x+2) and (x+3)

Conclusion 

Based on the previously mentioned facts in the overall study, it can be stated that the current study has discussed the quadratic equation. In the study, it has been found that the quadratic formula has been represented as the coefficient of the x2 where the value of the x is not equal to zero. Based on this primary discussion, the study has further included the determination process of minimum and maximum values of the quadratic equation. Moreover, the method and formulas are written in the study as well.