\[ a(1)^2 + b(1) + c = 2 \]
![\[ a(1)^2 + b(1) + c = 2 \]](https://soloferat.biz.id/images/a12--b1--c--2-.jpg)
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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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