How do you find the axis of symmetry, and the maximum or minimum value of the function #y = 6x^2 + 24x + 16#?

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Answer 1 · 2017-07-17T13:55:05

#x+2=0# is axis of symmetry and minimum value of #y=6x^2+24x+16# is #-8# at #x=-2#.

#y=6x^2+24x+16#

#=6(x^2+4x+4)-24+16#

#=6(x+2)^2-8#

As #6(x+2)^2# has minimum value #0# when #x=-2#

Minimum value of #y=6x^2+24x+16# is #-8#.

Further when #x=-2+-k#, #y=6k^2-8#

hence #y=6x^2+24x+16# is symmetric around #x=-2# and

#x=-2# or #x+2=0# is axis of symmetry.

graph{(6x^2+24x+16-y)(x+2)=0 [-4, 0, -10, 10]}