# Finding Axis of Symmetry in Quadratic Equation

For finding axis of symmetry in quadratic equation, use the following steps :1) Write the given equation in vertex form. [f(x) = a(x –h )

^{2}+ k ].

2) Use a completing square method.

**Examples :**

Write the following equation in vertex form .

1) f(x) = x

^{2}- 12 x + 46

**Solution :**

Here, a = 1 and b = -12

Add ~+mn~(–b)

^{2}/4a

^{2}= - (-12)

^{2}/4 = 144/4 =~+mn~36

f(x) = y =

__x__

^{2}- 12 x + 36__– 36 + 46__

**f(x) = ( x – 6 )**This is a vertex form.

^{2}+ 10**Coordinates of vertex = ( h, k ) = ( 6, 10)**

Axis of symmetry = x = 6

Axis of symmetry = x = 6

_________________________________________________________________

2) f(x) = x

^{2}+ 6x + 10

**Solution :**

Here a = 1 and b = 6

Add ~+mn~ (-b)

^{2}/4a

^{2}= (-6)

^{2}/4 = ~+mn~36/4 =~+mn~ 9

f(x) =

__x__

^{2}+ 6x + 9__– 9 + 10__

**f(x) = ( x + 3)**This is a vertex form.

^{2}+ 1**Coordinates of vertex = (h,k) = ( -3 , 1)**

Axis of symmetry = x = - 3

Axis of symmetry = x = - 3

______________________________________________________________________

3) f(x) = x

^{2}- 16

**Solution :**

Here a = 1 and b = 0

Add ~+mn~ (-b)

^{2}/4a

^{2}= 0

^{2}/4 = 0

**f(x) = x**This is a vertex form.

^{2}-16**Coordinates of vertex = (h,k) = ( 0 , -16 )**

Axis of symmetry = y = 0

Axis of symmetry = y = 0

**Introduction of Quadratic Equations**

• 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

• 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