How do you find the axis of symmetry, and the maximum or minimum value of the function #y= -x^2 + 2x + 1#?

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Answer 1 · 2016-02-03T05:37:17

The function has a maximum at #x=-1#

Axis of symmetry is -

#x=-1#

Given -

#y=-x^2+2x+1#

#dy/dx=-2x+2#
#(d^2y)/(dx^2)=-2#
#dy/dx=0=> -2x+2=0#

#x=2/(-2)=-1#

At #x=-1#; #dy/dx=0#;>#(d^2y)/(dx^2)<0#

Hence the function has a maximum at #x=-1#

Axis of symmetry is -

#x=-1#