Quadratic Functions:

Quadratic functions involve the second power of the variable but no higher power. The kinetic energy of a moving body is given by K.E. =1/2mv^2 , where m represents the mass and v represents the velocity of the object.

In general, A quadratic function is function that may be defined by the equation y=ax^2+bx+c, where a, b, and c are complex numbers constants or parameters, but a≠0. Notice that the restriction a≠0 assures that y=ax^2+bx+c defines a non-linear function.

The following equations define the quadratic functions:

1. y=x^2

2. y=-4x^2

3 y=x^2-6x+8

Quadratic Equations:

An equation in which the highest power of the variable i.e., degree is two is called a quadratic equation.

ax^2+bx+c=0, where a,b,c are constants, is a general quadratic equation.

Examples:

1. 5x^2+2x=0

2. x^2+2x-1=0

3. 58x^2+52x +6=0

4. 9x^2+6x-1=0

Consider the quadratic equations ax^2+bx+c=0, where a, b, c € R and a≠0

Roots of the equation is given by x=(-b±√(b^2-4ac))/2a .

What is plus/minus sign?

The plus/minus sign is used because every quadratic equation has maximum two solution.

Nature of Roots:

The nature of the roots, real or imaginary, depends on the b^2-4ac.

This is generally denoted by D also called Discriminant.

1. If D=0, Roots are real and equal.

2. If D>0, Roots are real and distinct.

3. If D<0, Roots are imaginary.