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

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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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