Vertex of the parabola y = x^2 — Algebra: find the vertex (result as integers)

Step-by-step solution to find the vertex of the parabola y = x^2. Uses the vertex formula and completing-the-square; answer is (0, 0).

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We want the vertex of the parabola y = x2.

  1. Using the vertex formula: For y = ax2 + bx + c the x-coordinate of the vertex is x = -b/(2a). Here a = 1 and b = 0, so x = -0/(2·1) = 0. Then y = 02 = 0.
  2. Completing the square (quick): y = x2 = (x - 0)2 + 0, so the vertex is at (0, 0).

Final answer: (0, 0)

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