# 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

2 /4a 2 = - (-12) 2 /4 = 144/4 =~+mn~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) = x
2 + 6x + 10

Solution :
Here a = 1 and b = 6

2 /4a 2 = (-6) 2 /4 = ~+mn~36/4 =~+mn~ 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) = x
2 - 16

Solution :
Here a = 1 and b = 0

2 /4a 2 = 0 2 /4 = 0

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

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

Axis of symmetry = y = 0