Given F(x) = -x^2 + 2x + 8 how would I complete the square

f(x) = - x² + 2x + 8
f(x) = (- x² + 2x) + 8
f(x) = - (x² - 2x) + 8
f(x) = - (x² - 2x + 1) + 8 - (- 1)
f(x) = - (x - 1)² + 8 + 1
f(x) = - (x - 1)² + 9
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Start out by grouping the x terms together:
F(x) = (-x^2 + 2x) + 8.

Factor out the x^2 coefficient (which is -1):
F(x) = -(x^2 - 2x) + 8.

Then, by completing the square by adding 1 within the parentheses and adding 1 on the outside:
F(x) = -(x^2 - 2x + 1) + 8 + 1
==> F(x) = -(x - 1)^2 + 9.

I hope this helps!

1) f(x) = -x^2 + 2x + 8

2) f(x) = - (x^2 - 2x + (2/2)^2 -(2/2)^2 ) + 8

3) f(x) = - [(x^2 - 2x + 1) - 1] + 8

4) f(x) = - [(x - 1)^2 - 1] + 8

5) f(x) = - (x - 1)^2 + 1 + 8

6) f(x) = - (x - 1)^2 + 9

-(x^2-2x-8)=
-(x-4)(x+2)

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