How do you graph and label the vertex and axis of symmetry of #y=2(x+1)^2+1#?

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Answer 1 · 2018-06-24T21:01:44

#(-1, 1)# & #x=-1#

The given equation:
#y=2(x+1)^2+1#

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

#(x+1)^2=\frac{1}{2}(y-1)#

Comparing above equation with standard form of upward parabola #X^2=4AY# we have

#X=x+1, \Y=y-1, \ A=\frac1{8} #

Now, the vertex of standard parabola: #X^2=4AY# is

#(X=0, Y=0)\equiv (x+1=0, y-1=0)\equiv (x=-1, y=1)#
hence, the vertex of given parabola is #(-1, 1)#

Now, the axis of symmetry of standard parabola: #X^2=4AY# is

#X=0#
#x+1=0#
#x=-1#

Hence the axis of symmetry of given parabola is #x=-1#