To convert the given equation to vertex form, we need to complete the square. The vertex form of a quadratic equation is (x - h)² + k, where (h, k) represents the coordinates of the vertex.
Let's break it down step by step:
1. Start with the given equation: (x - 2)² - 16.
2. To complete the square, we need to add a constant term that will allow us to factor a perfect square trinomial. In this case, we need to add 16 to both sides of the equation: (x - 2)² = 16.
3. Now, we can rewrite the equation in vertex form by factoring the perfect square trinomial: (x - 2)² = 4².
4. The vertex form of the equation is (x - h)² + k, where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. In this case, the vertex is (2, -16).
So, the equation in vertex form is (x - 2)² + (-16).
I hope that helps! Let me know if you have any more questions or if there's anything else I can assist you with.