Greatest value and completing the square

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Sasuto
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#1
Report Thread starter 1 month ago
#1
If f(x) = x^2 + 4x + 7 find
a) the smallest possible value of f(x)
b) the value of x for which this smallest value occurs
c) the greatest possible value of 1 / (x^2 + 4x + 7)


I have done parts (a) and (b) but not (c). I am also unsure of my answers for parts (a) and (b).

For (a) I got f(x) = -3 by completing the square

For (b) I got x = -2

If someone could help that would be great🙏
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flaurie
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#2
Report 1 month ago
#2
(Original post by Sasuto)
For (a) I got f(x) = -3 by completing the square
i'd have another think about your answer for (a), what did you get when you completed the square?
(b) is correct
Last edited by flaurie; 1 month ago
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Sasuto
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#3
Report Thread starter 1 month ago
#3
(Original post by flaurie)
i'd have another think about your answer for (a), what did you get when you completed the square?
(b) is correct
I got (x+2)^2 +3
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flaurie
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#4
Report 1 month ago
#4
(Original post by Sasuto)
I got (x+2)^2 +3
nice, so the smallest value of (x+2)^2 +3 would be when (x+2)^2 = 0 which leaves you with 3 (not -3)
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Sasuto
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#5
Report Thread starter 1 month ago
#5
(Original post by flaurie)
nice, so the smallest value of (x+2)^2 +3 would be when (x+2)^2 = 0 which leaves you with 3 (not -3)
So will the smallest value always be the term after the brackets?
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