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The equation of a parabola is y=x2+2x−7y = x^2 + 2x - 7. 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−7y = x^2 + 2x - 7. 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 transform the given equation into vertex form.\newlineThe given equation is y=x2+2x−7y = x^2 + 2x - 7. To complete the square, we need to add and subtract the square of half the coefficient of xx inside the parentheses.\newlineThe coefficient of xx is 22, so half of it is 11, and squaring it gives us 11. We add and subtract 11 to complete the square.\newliney=x2+2x+1−1−7y = x^2 + 2x + 1 - 1 - 7
  3. Rewrite equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants.\newliney=(x2+2x+1)−1−7y = (x^2 + 2x + 1) - 1 - 7\newliney=(x+1)2−8y = (x + 1)^2 - 8\newlineNow, the equation is in vertex form, where (h,k)=(−1,−8)(h, k) = (-1, -8).

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