SOLUTION: Dear Math Tutor, Please help me with: Write x^2 + 10x + 38 in the form (x+b)^2+c where the values of b and c are to be found. a) State the minimum value of x^2 + 10x + 38 and

Question 879489: Dear Math Tutor,
Please help me with: Write x^2 + 10x + 38 in the form (x+b)^2+c where the values of b and c are to be found.
a) State the minimum value of x^2 + 10x + 38 and the value of x for which this occurs.
b) Determine the values of x for which x2+10x+38 is greater than or equal to 22.
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Completed square form of x^2 + 10x + 38 is (x+5)^2 + 13
therefore b=-5 and c=13
a) minimum value of x^2 + 10x + 38 is x less than or equal to 13
b) 12x+38=22
x=-1 and 1/3 or -4/3
so values for which x2+10x+38 is greater than or equal to 22 is x must be greater than or equal to -4/3.
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Is all of that correct? I cant help but feel Im missing something as its out of 12 marks.
Please advise,
With gratitude
Nat

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
x^2 + 10x + 38 = (x+5)^2 + 13 Nice Work
a) minimum value of x^2 + 10x + 38 is 13 when x = -5
b) 22 ≤ (x+5)^2 + 13
9 ≤ (x+5)^2
�3 ≤ x+5
-8 ≤ x ≤ -2

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