Complete the square to re-write the quadratic function in vertex form:y, equals, minus, 2, x, squared, plus, 12, x, minus, 27y=−2x 2 +12x−27

Sure, here are the steps to complete the square and rewrite the quadratic function in vertex form:

1. The general form of a quadratic function is y = ax^2 + bx + c. In this case, a = -2, b = 12, and c = -27.

2. The vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

3. To convert the general form to the vertex form, we can complete the square. Here are the steps:

   • First, factor out the coefficient of x^2 (which is -2) from the first two terms: y = -2(x^2 - 6x) - 27.

   • Next, to complete the square inside the parentheses, take half of the coefficient of x, square it, and add it inside the parentheses. Half of -6 is -3, and (-3)^2 = 9. So we add and subtract 9 inside the parentheses: y = -2(x^2 - 6x + 9 - 9) - 27.

   • This gives us: y = -2[(x - 3)^2 - 9] - 27.

   • Distribute the -2: y = -2(x - 3)^2 + 18 - 27.

   • Simplify the constants: y = -2(x - 3)^2 - 9.

So, the vertex form of the given quadratic function is y = -2(x - 3)^2 - 9.