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 = 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
Add ~+mn~ (-b) 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
Add ~+mn~ (-b) 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
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