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What is the axis of symmetry and vertex for the graph #f(x)=2x^2-4x+1#?

Answer 1

vertex at #(x,y)=(1,-1)#
axis of symmetry: #x=1#

We will convert the given equation into "vertex form"
#color(white)("XXX")y=color(green)m(x-color(red)a)^2+color(blue)b#
where
#color(white)("XXX")color(green)m# is a factor related to the horizontal spread of the parabola; and
#color(white)("XXX")(color(red)a,color(blue)b)# is the #(x,y)# coordinate of the vertex.

Given:
#color(white)("XXX")y=2x^2-4x+1#

#color(white)("XXX")y=color(green)2(x^2-2x)+1#

#color(white)("XXX")y=color(green)2(x^2-2x+color(magenta)1)+1-(color(green)2xxcolor(magenta)1)#

#color(white)("XXX")y=color(green)2(x-color(red)1)^2+color(blue)((-1))#

The vertex form with vertex at #(color(red)1,color(blue)(-1))#

Since this equation is of the form of a parabola in "standard position"
the axis of symmetry is a vertical line passing though the vertex, namely:
#color(white)("XXX")x=color(red)1#

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Answer 2

Kennedy Adams

The axis of symmetry for the graph of ( f(x) = 2x^2 - 4x + 1 ) is ( x = 1 ), and the vertex is ( (1, -1) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.