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The equation of a parabola is y=x2+2x+6y = x^2 + 2x + 6. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______

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Full solution

Q. The equation of a parabola is y=x2+2x+6y = x^2 + 2x + 6. 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+6y = x^2 + 2x + 6.
  3. Complete the Square: Complete the square by adding and subtracting (22)2(\frac{2}{2})^2, which is 11, to the equation.y=x2+2x+1−1+6y = x^2 + 2x + 1 - 1 + 6
  4. Rewrite Equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. \newliney=(x2+2x+1)−1+6y = (x^2 + 2x + 1) - 1 + 6
  5. Factor and Simplify: Factor the perfect square trinomial and simplify the constants.\newliney=(x+1)2+5y = (x + 1)^2 + 5

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