How do I convert $f (x) = - 2 x^{2} + 2 x + 4$ $f (x) = -2x^2 + 2x + 4$ 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

$(y - \frac{9}{2}) = - 2 {(x - \frac{1}{2})}^{2}$ $(y-9/2)= -2(x-1/2)^2$

Given f(x)= y= $- 2 x^{2} + 2 x + 4$ $-2x^2 +2x+4$

= $- 2 (x^{2} - x) + 4$ $-2(x^2 -x) +4$

= $- 2 (x^{2} - x + \frac{1}{4} - \frac{1}{4}) + 4$ $-2(x^2 -x + 1/4 -1/4)+4$

= $- 2 (x^{2} - x + \frac{1}{4}) + \frac{1}{2} + 4$ $-2(x^2 -x +1/4)+1/2 +4$

= $- 2 {(x - \frac{1}{2})}^{2} + \frac{9}{2}$ $-2(x-1/2)^2 +9/2$

$y - \frac{9}{2} = - 2 {(x - \frac{1}{2})}^{2}$ $y -9/2= -2(x-1/2)^2$ , which is required standard form.