Axis of symmetry of y = x^2 − 2x − 1/4 — find the equation (step-by-step)

Find the vertical axis of symmetry for the parabola y = x^2 − 2x − 1/4. Step-by-step solution using the formula x = -b/(2a) and completing the square. Final answer: x = 1.

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For a parabola y = ax^2 + bx + c the axis of symmetry is the vertical line x = -b/(2a).

  1. Identify coefficients: a = 1, b = -2.
  2. Use the formula: x = -b/(2a) = -(-2)/(2·1) = 2/2 = 1.
  3. (Check by completing the square) y = x^2 - 2x - 1/4 = (x-1)^2 - 1 - 1/4 = (x-1)^2 - 5/4, so the vertex is at (1, -5/4) and the axis is x = 1.

Answer: x = 1.

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