\[ a(1)^2 + b(1) + c = 2 \]

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• An entomologist studying the flight dynamics of bees models their path as a parabola described by \(y = ax^2 + bx + c\). If the path passes through the points (1, 2), (2, 3), and (3, 5), find the coefficients \(a\), \(b\), and \(c\).
• To find the coefficients \(a\), \(b\), and \(c\), substitute each point into the parabola equation \(y = ax^2 + bx + c\).
• For (1, 2):
• \[ a + b + c = 2 \] — (Equation 1)
• For (2, 3):
• \[ a(2)^2 + b(2) + c = 3 \]

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