Let function \( f(x) \) be defined as \( f(x)=x^{2}+b x+c \), where...

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Let function \( f(x) \) be defined as \( f(x)=x^{2}+b x+c \), where \( b, c \) are real numbers and \( f(1)-2 f(5)+f(9)=32 \). Number of ordered pairs \( (b, c) \) such that \( |f(x)| \leq 8 \) for all \( x \)
\( \mathrm{P} \) in the interval \( [1,9] \).

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