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5**Question:** A programmer is analyzing medical image data, where pixel intensity \( I(x) \) at position \( x \) is modeled as \( I(x) = ax^2 + bx + c \). Given that \( I(1) = 6 \), \( I(2) = 11 \), and \( I(3) = 18 \), determine the values of \( a \), \( b \), and \( c \).
We have three conditions given by the pixel intensities:
\( I(1) = a(1)^2 + b(1) + c = 6 \)
\( I(2) = a(2)^2 + b(2) + c = 11 \)