Question 485388
Find the minimum or maximum point of the following parabola by using the completing square method.

f(x)=-x^2+10x-28

the following is my working..I am not sure whether it is correct..please advise..
f(x)=-x^2+10x-28
= -x^2 + 10x + (10/2 )^2  - (10/2 )^2  - 28
= -(x+5)2 -53

From -(x+5)2 -53, compare with a(x-h)^2 +k
h= -5, k= -53, since a <0, so it has a maximum point at (-5,-53).
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-x^2+10x-28 = 0
-(x^2 -10x) = 28
-(x^2 - 10x + 25) = 3 ( -25 is added to both sides)
-(x-5)^2 - 3 = 0
--> (5,-3)
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to check:
Line of Symmetry is x = -b/2a
x = -10/-2 = 5
f(5) = -3
--> (5,-3)
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Completing the square is the worst method.  Avoid it if possible.