We at **ask-math **believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

**We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.**

**Affiliations with Schools & Educational institutions are also welcome.**

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

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

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers