For a quadratic y = ax^2 + bx + c, the x-coordinate of the vertex is

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Multiple Choice

For a quadratic y = ax^2 + bx + c, the x-coordinate of the vertex is

Explanation:
The x-coordinate of the vertex is where the parabola’s axis of symmetry sits. For y = ax^2 + bx + c, that point occurs 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/(2a))^2] + c = a(x + b/(2a))^2 + c - b^2/(4a). The square term is minimized (or maximized) when x + b/(2a) = 0, so x = -b/(2a). Another check is via calculus: dy/dx = 2ax + b, set to zero to find the critical point, giving x = -b/(2a). In all cases, the x-coordinate of the vertex is -b/(2a), provided a ≠ 0.

The x-coordinate of the vertex is where the parabola’s axis of symmetry sits. For y = ax^2 + bx + c, that point occurs 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/(2a))^2] + c = a(x + b/(2a))^2 + c - b^2/(4a). The square term is minimized (or maximized) when x + b/(2a) = 0, so x = -b/(2a). Another check is via calculus: dy/dx = 2ax + b, set to zero to find the critical point, giving x = -b/(2a). In all cases, the x-coordinate of the vertex is -b/(2a), provided a ≠ 0.

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