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The equation of a parabola is y=x2+6x+14y = x^2 + 6x + 14. 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+6x+14y = x^2 + 6x + 14. 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 Equation: Start with the given equation y=x2+6x+14y = x^2 + 6x + 14.
  3. Complete the Square: Complete the square by adding and subtracting (62)2(\frac{6}{2})^2, which is 99, to the equation.\newliney=x2+6x+9+14−9y = x^2 + 6x + 9 + 14 - 9
  4. Rewrite Equation: Rewrite the equation grouping the perfect square trinomial and combining the constants.\newliney=(x2+6x+9)+14−9y = (x^2 + 6x + 9) + 14 - 9\newliney=(x+3)2+5y = (x + 3)^2 + 5
  5. Final Vertex Form: The equation in vertex form is y=(x+3)2+5y = (x + 3)^2 + 5.

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