For f(x) = 3x^2 - 5x + 2, find the vertex.

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Multiple Choice

For f(x) = 3x^2 - 5x + 2, find the vertex.

Explanation:
The vertex of a quadratic in standard form y = ax^2 + bx + c lies at x = -b/(2a). Here a = 3 and b = -5, so x = -(-5)/(2×3) = 5/6. Evaluate the function at that x to get the y-coordinate: f(5/6) = 3(5/6)^2 - 5(5/6) + 2 = 3(25/36) - 25/6 + 2 = 25/12 - 50/12 + 24/12 = -1/12. The vertex is (5/6, -1/12). Since a > 0, the parabola opens upward, so this is the minimum point.

The vertex of a quadratic in standard form y = ax^2 + bx + c lies at x = -b/(2a). Here a = 3 and b = -5, so x = -(-5)/(2×3) = 5/6. Evaluate the function at that x to get the y-coordinate: f(5/6) = 3(5/6)^2 - 5(5/6) + 2 = 3(25/36) - 25/6 + 2 = 25/12 - 50/12 + 24/12 = -1/12. The vertex is (5/6, -1/12). Since a > 0, the parabola opens upward, so this is the minimum point.

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