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).
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 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).
-------------------
-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)
--------------------
to check:
Line of Symmetry is x = -b/2a
x = -10/-2 = 5
f(5) = -3
--> (5,-3)
-----------
Completing the square is the worst method. Avoid it if possible.
|
|
|
