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We need to complete the square in order to write g(x) in vertex form:

g(x) = -2( x^2 - 2 x + 2)

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

= -2(x-1)^2 -2

And the vertex is at the point (h,k) in this case, (1,-2)

g(x) = -2( x^2 - 2 x + 2) so this is the quadratic function in form

g(x) = -2(x-1)^2 -2 is the equation in vertex form

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