Question

Which function has an axis of symmetry of x = −2?

Answer 1

Given : 4 Functions f(x) and has axis of symmetry of x = - 2

To find :  Which function has axis of symmetry of x = - 2

Solution:

f(x) = (x − 1)² + 2

f(x) = (x 1)² − 2

f(x) = (x − 2)² − 1

f(x) = (x + 2)² − 1

f(x)=a(x-h)²+k

will have symmetry  

an axis of symmetry of x = h

putting h = -2

=> f(x) = a(x-(-2) )²+k

=> f(x) = a(x + 2)² + k

Comparing with given Equations

f(x) = (x + 2)² − 1 meets it

hence function   f(x) = (x + 2)² − 1  has an axis of symmetry of x = −2

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