Completing the square seems to be the hardest thing for me to do. ???? It seems the set of rules in my text book and examples online are never followed by the actual problems in my book. I know this is a BASIC concept, that is why it is very frustrating to not understand it. Seems very counter-intuitive for some reason. Anyway, here it is Write in std form and find vertex. (I can evaluate, once in std form just fine) -x^2-4x+4=0 Applying the rules in the book and online, the answer should be what we started with. I am lost. Please help with a step by step solution. Thank you
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-x^2-4x+4
-(x^2+4x) + 4
-(x^2 + 4x + 4 - 4) +4
-((x+2)^2-4)+4
-(x+2)^2+8
The vertex is (-2,8)
For x^2 +bx + c,
You will always take out half of b and use (x + (b/2)^2
Now to evaluate,
-(x+2)^2+8=0
(x+2)^2=8
(x+2)= +/- sq(8)
x = -2 +/- sq(8)
or x= -2 +/- 2sq(2)
-(x^2+4x) + 4
-(x^2 + 4x + 4 - 4) +4
-((x+2)^2-4)+4
-(x+2)^2+8
The vertex is (-2,8)
For x^2 +bx + c,
You will always take out half of b and use (x + (b/2)^2
Now to evaluate,
-(x+2)^2+8=0
(x+2)^2=8
(x+2)= +/- sq(8)
x = -2 +/- sq(8)
or x= -2 +/- 2sq(2)