Select the description of the graph created by the equation 3x2 – 6x + 4y – 9 = 0.

Rearrange and complete the square: 3(x² − 2x) + 4y − 9 = 0 becomes 3(x − 1)² + 4y − 12 = 0. Thus (x − 1)² = −(4/3)(y − 3), which has vertex (1, 3). The negative coefficient means the parabola opens downward, so the correct description is “Parabola with a vertex at (1, 3) opening downward.”

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