# Finding Axis of Symmetry in Quadratic Equation

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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) = x2 - 12 x + 46

Solution :
Here, a = 1 and b = -12

Add ±(–b)2/4a2 = - (-12)2/4 = 144/4 =±36

f(x) = y = x2 - 12 x + 36 – 36 + 46

f(x) = ( x – 6 ) 2 + 10 This is a vertex form.

Coordinates of vertex = ( h, k ) = ( 6, 10)

Axis of symmetry = x = 6

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2) f(x) = x2 + 6x + 10

Solution :
Here a = 1 and b = 6

Add ± (-b)2/4a2 = (-6)2/4 = ±36/4 =± 9

f(x) = x2 + 6x + 9 – 9 + 10

f(x) = ( x + 3) 2 + 1 This is a vertex form.

Coordinates of vertex = (h,k) = ( -3 , 1)

Axis of symmetry = x = - 3

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3) f(x) = x2 - 16

Solution :
Here a = 1 and b = 0

Add ± (-b)2/4a2 = 02/4 = 0

f(x) = x2 -16 This is a vertex form.

Coordinates of vertex = (h,k) = ( 0 , -16 )

Axis of symmetry = y = 0