How do you write the quadratic in vertex form given #f(x) = -3x^2 + 6x -2#?

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Answer 1 · 2015-04-29T07:43:49

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=-3x^2+6x-2#

#-> y + 2 = -3x^2 + 6x# (Transposed -2 to the Left Hand Side)

#-> y + 2 = -3(x^2 - 2x)# (Made the coefficient of #x^2# as 1)

Now we subtract #3# from each side to complete the square

#-> y + 2 - 3 = -3(x^2 - 2x + 1^2)#

#-> y - 1 = -3(x-1)^2 #

# -> color(green)(y = -3{x - 1}^2 + 1# is the Vertex Form

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