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

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Answer 1 · 2016-04-04T19:30:26

#color(blue)("Axis of symmetry is "x=-1)#

#color(blue)("It is a minimum "->(x,y)->(-1,0))#

Consider standard equation form #y=ax^2+bx+c#

Your equation is in standard vertex form of #y=a(x+b/(2a))^2+c#

Where #a=1" and "c=0# and #x_("vertex") = (-1)xxb/(2a)#

#x_("vertex") =(-1)xx(1) = -1#. This is also the axis of symmetry.

#color(blue)("So axis of symmetry is "x=-1)#

#color(brown)("The coefficient of "x" is +1 ie positive. So the graph is of")##color(brown)("general shape "uu", thus we have a minimum.")#

#x_("minimum")=x_("vertex")=-1#

Thus by substitution

#y_("minimum")=(x_("vertex")+1)^2#

#y_("minimum")=(-1+1)^2 = 0#

#color(blue)("So the minimum "->(x,y)->(-1,0))#

Tony B