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


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

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