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The equation of a parabola is y=x2+2x−8y = x^2 + 2x - 8. 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−8y = x^2 + 2x - 8. 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, which is y=a(x−h)2+ky = a(x - h)^2 + k.
  2. Start with given equation: Start with the given equation y=x2+2x−8y = x^2 + 2x - 8.
  3. Complete the square: Complete the square by adding and subtracting (22)2(\frac{2}{2})^2, which is 11, to the equation.\newliney=x2+2x+1−1−8y = x^2 + 2x + 1 - 1 - 8
  4. Rewrite equation: Rewrite the equation grouping the perfect square trinomial and combining the constants.\newliney=(x2+2x+1)−1−8y = (x^2 + 2x + 1) - 1 - 8\newliney=(x+1)2−9y = (x + 1)^2 - 9

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