What is the axis of symmetry and vertex for the graph #y=-x^2+4x+1#?

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Answer 1 · 2017-10-26T17:31:56

axis of symmetry: #x = 2#
vertex: #(2,5)#

convert #-x^2+4x+1# into #p(x+q)^2+r# form:

#-x^2+4x+1 = -(x^2-4x-1)#

#x^2-4x-1 = (x^2-4x+4)-5#

#=(x-2)^2-5#

#-(x^2-4x-1)=-((x-2)^2-5) = -(x-2)^2+5#

#p(x+q)^2+r = -(x-2)^2+5#

#p = 1, q = -2, r = 5#

axis of symmetry: #x = -q#

here, #x = 2#

coordinates of vertex: #(-q, r)#

here, this is #(2, 5)#