How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #f(x)=x^2-5x+6#?

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Answer 1 · 2017-11-18T08:45:25

axis symmetry #X=5/2#

#f_min(5/2)=-1/4#

graph below

firstly we complete the square

#f(x)=x^2-5x+6#

#f(x)=x^2-5x+color(red)((5/2)^2)-(5/2)^2+6#

#f(x)=(x-5/2)^2-25/4+6#

#f(x)=(x-5/2)^2-1/4#

axis of symetry is when bracket#=0#

#X=5/2#

now #(x-5/2)^2>=0" " AAx inRR#

#:.f(x)>=-1/4#

min at #f(5/2)=-1/4# graph{x^2-5x+6 [-10, 10, -5, 5]}