Question: A parabola with equation y = ax 2 + bx + c passes through the point (1, 3) . It is also known that a

A parabola with equation

y = ax2 + bx + c

passes through the point

(1, 3)

. It is also known that a tangent line to the parabola has slope

3

at x = 1, and another tangent line to the parabola has slope

17

at x = 1. Determine the coefficients a, b, and c and write the equation of this parabola.

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