asymptotic tight bound for quadratic functions

Question

In CLRS (Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein), for a function

f(n) = an² + bn

Answer 1

P(n) = an² + bn + c = an²( 1 + b / ( an ) + c / ( an² )) = an²( 1 ± ( | b | / a ) / n ± ( √( | c | / a ) / n )²
so if we take for example q = max( | b | / a, √( | c | / a )) than
P(n) ≤ an²( 1 + ( q / n ) + ( q / n )² ) and if we take n₀ = q than we'll get the second constant
c₂ = 3a analogically for the lower bound