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

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Answer 1 · 2018-02-28T21:16:45

#(1,1)# #-># local maximum.

Putting the equation in vertex form,

#y=-x^2+2x#

#y=-[x^2-2x]#

#y=-[(x-1)^2-1]#

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

In vertex form, the #x# coordinate of the vertex is the value of #x# which makes the square equal to #0#, in this case, 1 (since #(1-1)^2 = 0#).

Plugging this value in, the #y# value turns out to be #1#.

Finally, since it is a negative quadratic, this point #(1,1)# is a local maximum.