How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #f(x)=x^2-2x-1#?

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Answer 1 · 2017-07-23T07:49:06

#f(x)_min=-1#

line of symmetry#" "X=1#

You need to complete the square first before answering this question

#f(x)=x^2-2x-1#

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

#f(x)=(x-1)^2-1-1#

#:.f(x)=(x-1)^2-2#

since we have a #+x^2" "#term the function will have a minimum.

this will be when #(x-1)^2" "#term#=0#

#:." minimum "is -2#

the coordinates for the minimum#(1,-2)#

the axis of symmetry is the line through the vertex #ie. X=1#

the results can be seen on the graph below

graph{x^2-2x-1 [-10, 10, -5, 5]}