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The equation of a parabola is y=x2−2x+11y = x^2 - 2x + 11. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______

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Q. The equation of a parabola is y=x2−2x+11y = x^2 - 2x + 11. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______
  1. Identify vertex form: Identify the vertex form of a parabola.\newlineThe vertex form of a parabola is given by y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola.
  2. Complete the square: Complete the square to rewrite the equation in vertex form.\newlineWe have the equation y=x2−2x+11y = x^2 - 2x + 11. To complete the square, we need to find the value that makes x2−2xx^2 - 2x a perfect square trinomial. We do this by taking half of the coefficient of xx, squaring it, and adding it to and subtracting it from the equation.\newlineHalf of the coefficient of xx is −2/2=−1-2/2 = -1. Squaring this gives us (−1)2=1(-1)^2 = 1. We add and subtract 11 to the equation.\newliney=x2−2x+1+11−1y = x^2 - 2x + 1 + 11 - 1
  3. Rewrite and simplify: Rewrite the equation with the perfect square trinomial and simplify.\newlineNow we have y=(x2−2x+1)+11−1y = (x^2 - 2x + 1) + 11 - 1, which simplifies to y=(x−1)2+10y = (x - 1)^2 + 10.

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