\( h(0) = 3 \) implies \( c = 3 \).

February 22, 2026

$\( h(0) = 3 \) implies \( c = 3 \).$

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#### 3,375,000**Question: A herpetologist studying reptile population dynamics models the growth of a lizard population with a quadratic polynomial \( h(x) \) such that \( h(0) = 3 \), \( h(1) = 8 \), and \( h(2) = 15 \). Find \( h(x^2 + 2) \).
\( h(1) = 8 \) gives us \( a(1)^2 + b(1) + 3 = 8 \) which simplifies to \( a + b + 3 = 8 \). Thus, \( a + b = 5 \).
\( h(2) = 15 \) gives us \( a(2)^2 + b(2) + 3 = 15 \) which simplifies to \( 4a + 2b + 3 = 15 \). Thus, \( 4a + 2b = 12 \).
\( a + b = 5 \)

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