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A polynomial equation of second degree is called a Quadratic Equations.The standard form of the equation is ax

1) x

2) 4a

3) 2/3p

x

The constant ‘a' assuming the value zero reduces the equation to linear form.

When we graph such equation, we get a parabola.

Example : f(x) = x

The above graph is a upward graph with lowest point known as the

The points where graph cut the X- axis represent the zeros of the function. The X- coordinates give the

Thus x = α is a roots of P(x) = 0 if and only if P(α)= 0

1) |
Standard form :a ^{2}+ bx + c =0 |
Used to find roots of the equation. |

2) |
Vertex form a(x-h) ^{2} + k |
Used to draw a parabola |

3) |
Factored form : a(x - x1)(x - x2)= 0 |
Roots are x1 and x2 |

There are different methods to factoring the Quadratic Equations.

1) 4x

It is a quadratic equation since the highest degree is 2.

2) x - 1/x = x

x - 1/x = x

(x

∴ x

∴ -x

The degree of the equation is 3 so its not a quadratic equation.

3) 5 - x(x - 3) = 0

5 - x(x - 3) = 0

5 - x

The degree of the equation is 2 so its a quadratic equation.

According to the equation, a=-1,b=3 and c=5

the axis of symmetry is x = x-coordinate of vertex.

x-coordinate of vertex = -b/2a

x = 3/(-2 x 1)

x = -3/2

x = -1.5

∴

• Splitting of middle term

• By completing the square

• Factorization using Quadratic Formula

• Vertex form from Quadratic Equation

• Finding Axis of Symmetry in Quadratic equation

• Solved Problems on Quadratic Equation

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