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a(2)^2 + b(2) + c = 960 \Rightarrow 4a + 2b + 1013 = 960 \Rightarrow 4a + 2b = -53 \quad ext{(2)}
From (1): \( a + b = -13 \)
Multiply (1) by 2: \( 2a + 2b = -26 \)
Subtract from (2):
rac{27}{2} + b = -13 \Rightarrow b = -13 + rac{27}{2} = rac{-26 + 27}{2} = rac{1}{2}
Now compute \( a + b + c \):
a + b + c = - rac{27}{2} + rac{1}{2} + 1013 = rac{-26}{2} + 1013 = -13 + 1013 = 1000
oxed{1000}
A community health researcher studies nutrient concentration in soil, modeled by \( N(x) = rac{x^3 - 8}{x - 2} \). Find \( N(3) \) in simplest form and determine whether the function is defined at \( x = 2 \).
First, simplify \( N(x) = rac{x^3 - 8}{x - 2} \). Recognize the numerator as a difference of cubes: