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This question requires the use of Completing the Square:
5 – 2x – x^2 = -1 ( x^2 + 2x – 5)
= -1 (x^2 + 2x + 1 – 6)
= -1 (x^2 + 2x + 1) + 6
= 6 – (x+1)^2, p =6 and q =1
(a) You can solve this graphically:
The maximum value will be at y=6
Alternatively, since (x+1)^2 has to be a non-negative value, the expression is at its maximum value when (x+1)^2 = 0. Thus, maximum value = 6
(b) 5 – 2x – x^2 = 0
Hence, 6 – (x+1)^2 = 0
(x+1)^2 = 6
(x+1) = +- sqrt 6
x = sqrt 6-1 or -sqrt 6-1//
Alternatively, use the quadratic formula and sub in a = -1, b = -2, c = 5