How do I convert #f (x) = -2x^2 + 2x + 4# to standard form ?

Question

I understand how to complete the square, but this leaves me with (-2x + 4) (x+1). I thought I needed to have a perfect square ?

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Answer 1 · 2016-11-26T18:00:38

#(y-9/2)= -2(x-1/2)^2#

Given f(x)= y= #-2x^2 +2x+4#

= #-2(x^2 -x) +4#

=#-2(x^2 -x + 1/4 -1/4)+4#

= #-2(x^2 -x +1/4)+1/2 +4#

=#-2(x-1/2)^2 +9/2#

#y -9/2= -2(x-1/2)^2#, which is required standard form.