Graphing Quadratic Equations

Graphing of the quadratic equation also helps to determine the intercept point in the curve for determining the upward and downward slope of the graph. Graphing of the quadratic equation can be determined from the function of f(x)=x2 and the curve is a parabola in the graph. If the equation changes to f(x)=ax2, then the large value of x represents the curve in the inward direction and the smaller number represents the outward direction of the curve.

What is a Quadratic Equation?

A quadratic equation is the algebraic polynomial equation that has positive variables and coefficients and is denoted by the below formula:

ax2 + bx + c= 0

Here a and b is the coefficient in the equation, x is the variable and c is the constant.

A quadratic equation is also defined as the equation of degree 2 and it is calculated by the formula of multiplication and factor. In the above equation, there are two roots and the roots can be equal to each other. The properties of the quadratic equation suggest that the value of the roots cannot be equal to zero in the equation.

Explain Graph of Quadratic Equation

The graph of the quadratic equation is a parabola and it has a curved shape in the graphical representation. The main points of the parabola are defined as the vertex and the vertex can be denoted as the highest or lowest point in the parabola. Determination of vertex in the graph and the symmetry axis depends on the below equation:

y= a (x-h)2+k

The vertex h and k can be determined in two ways is = (-b/2a,-d/4a), here, d= b2-4ac

From the above equation, the value of h is calculated by h=-b/2a and it is required to evaluate y at h to determine the value of k.

Solving of Quadratic Equation

Let the quadratic equation is 2x2-5x+3=0, therefore the solution can be determined by below formula:

2x2-5x+3=0

2x2-2x-3x+3=0

2x(x-1)-3(x-1) =0

(2x-3) (x-1) =0

Therefore 2x-3=0, x=3/2, x-1=0, x=1 

From the above example, it is clear that the value of x2 is positive; therefore the vertex of the graph will be at the bottom of the parabola. Moreover, 3/2 and 1 are the two roots of the above equation. 

Vertex of Quadratic Equation

The vertex of the quadratic equation is defined as the coordinating point where the parabola crosses the axis of the symmetry. The vertex formula helps to determine the point of coordination between the two values in the equation.

• f(x)= ax2 + bx + c – in this equation the parabola opens up as the value of a is positive
• f(x)= -ax2 + bx + c – in this equation the parabola is opens down as the value of a is negative

What are the Different Forms of Quadratic Equations?

Three different forms of a quadratic equation are denoted as below equation:

• The standard form of the quadratic equation is f(x)= ax2 + bx + c
• The factored form of the quadratic equation is y= a (x-r1) (x-r2)
• The vertex form of the quadratic equation is y= a (x-h)2+k. Here h and k are the two vertex points
• The positive value of a and degree 2 will represent the parabola in an upward direction

Properties of Quadratic Equation

The main property of the standard quadratic equation is that the highest degree of the root will be 2 and it determines the properties of the parabola curve in the vertex equation. The roots of the equation can be determined by the formula of the algebraic equation. The vertex point of the parabola depends on the discriminant d= b2-4ac. The value of h and k can be denoted as -b/2a and -d/4a. The value of coefficient in the quadratic equation will not be equal to zero.

Conclusion

The above study indicates that the graphical representation of the quadratic equation helps to determine the point of coordination between a symmetry axis and vertex point in the graph. The positive value of a helps to denote the graph in the upward direction and the negative value of a helps to denote the graph in the downward direction. The value of the coefficient also determines the point of coordination in the vertex equation in the parabola. A quadratic equation is a 2-degree equation as the value of roots will be the highest 2.