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The equation of a parabola is y=x2+2x−4y = x^2 + 2x - 4. 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−4y = x^2 + 2x - 4. 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. The 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−4y = x^2 + 2x - 4. To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with x2+2xx^2 + 2x.\newlineThe value needed is (2/2)2=1(2/2)^2 = 1. We add and subtract 11 inside the equation.
  3. Add Value Found: Add and subtract the value found in Step 22 to the equation.\newliney=x2+2x−4y = x^2 + 2x - 4\newliney=x2+2x+1−1−4y = x^2 + 2x + 1 - 1 - 4\newlineNow, group the perfect square trinomial and the constants.
  4. Rewrite Equation: Rewrite the equation with the perfect square trinomial and combine the constants.\newliney=(x2+2x+1)−1−4y = (x^2 + 2x + 1) - 1 - 4\newliney=(x+1)2−5y = (x + 1)^2 - 5\newlineNow, the equation is in vertex form, where the vertex is (−1,−5)(-1, -5).

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