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

f(n) = an2 + bn + c

they said

Suppose we take the constants c1 = a/4, c2 = 7a/4, and n0 = 2·max(|b|/a, √(|c|/a)).
Then 0 ≤ c1n2 ≤ an2 + bn + c ≤ c2n2 for all n ≥ n0.
Therefore f(n) is Θ(n2).

But they didn't specify how values of these constants came ?
I tried to prove it but couldn't.
Please tell me how these constants came ?

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