How do you write #y=4x^2-4x+2# into vertex form?

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Answer 1 · 2015-04-30T12:52:53

The vertex form of a quadratic function is given by
#y = a(x - h)^2 + k#, where #(h, k)# is the vertex of the parabola.

We can use the process of Completing the Square to get this into the Vertex Form.

#y=4x^2-4x+2#

#-> y - 2 = 4x^2 - 4x# (Transposed 2 to the Left Hand Side)

#-> y - 2 = 4(x^2 - x)# (Made the coefficient of #x^2# as 1)

Now we add #1# from each side to complete the square

#-> y - 2 + 1 = 4{x^2 - x + (1/2)^2}#

#-> y - 1 = 4(x-1/2)^2 #

#-> color(green)( y = 4(x-1/2)^2 + 1# is the Vertex Form

The vertex of the Parabola is# {0.5 , 1}#