What is the axis of symmetry for f(x) = −3x2 + 12x − 6?

The axis of symmetry can be found by finding the average of the zeros, a derivation from the conservation of energy :P, or by finding the point when the velocity is equal to zero.

df/dx=-6x+12 so df/dx, velocity, equals zero when:

-6x+12=0

6x=12

x=2  so the axis of symmetry is the vertical line x=2



average of zeros...

3x^2-12x+6=0

x^2-4x+2=0

x^2-4x=-2

x^2-4x+4=2

(x-2)^2=2

x-2=±√2

x=2±√2  so the average of the zeros is obviously 2.



conservation of energy

vf-vi=at  When vf=0, this is the maximum value for f(x)...

-vi=at, vi=b and a(acceleration)=2a(from quadratic) and t=x

-b=2ax

x=-b/(2a)  in this case

x=-12/(2(-3))

x=-12/-6

x=2

 

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