The vertex of the parabola y = ax^2 + bx + c occurs at x = -b/(2a). Which statement is correct?

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Multiple Choice

The vertex of the parabola y = ax^2 + bx + c occurs at x = -b/(2a). Which statement is correct?

Explanation:
For a quadratic y = ax^2 + bx + c with a ≠ 0, the vertex sits on the axis of symmetry at x = -b/(2a). You can see this by completing the square: y = a[x^2 + (b/a)x] + c = a(x + b/(2a))^2 - b^2/(4a) + c. The squared term is zero at x = -b/(2a), which is where the vertex lies. In the vertex form y = a(x - h)^2 + k, the vertex is at (h, k), and comparing gives h = -b/(2a). So the statement that the vertex occurs at x = -b/(2a) is the correct one. The other options don’t match the x-coordinate of the vertex (they miss the negative sign, swap signs, or refer to a non-parabola case).

For a quadratic y = ax^2 + bx + c with a ≠ 0, the vertex sits on the axis of symmetry at x = -b/(2a). You can see this by completing the square: y = a[x^2 + (b/a)x] + c = a(x + b/(2a))^2 - b^2/(4a) + c. The squared term is zero at x = -b/(2a), which is where the vertex lies. In the vertex form y = a(x - h)^2 + k, the vertex is at (h, k), and comparing gives h = -b/(2a). So the statement that the vertex occurs at x = -b/(2a) is the correct one. The other options don’t match the x-coordinate of the vertex (they miss the negative sign, swap signs, or refer to a non-parabola case).

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