Answer:
Therefore, the correct answer is A) (x - 1)^2 - 9. This is the vertex form of the given quadratic equation. The vertex of the parabola represented by this equation is (1, -9).
Explanation:
The quadratic equation y = x^2 - 2x - 8 can be written in vertex form as (x - 1)^2 - 9.
To understand why this is the case, let's go through the process step by step:
1. The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
2. To find the vertex form, we need to complete the square. We can do this by focusing on the terms involving x.
3. In the given equation y = x^2 - 2x - 8, we see that the coefficient of x^2 is 1, the coefficient of x is -2, and the constant term is -8.
4. To complete the square, we need to take half of the coefficient of x and square it. In this case, half of -2 is -1, and (-1)^2 is 1.
5. We can rewrite the equation as y = (x^2 - 2x + 1) - 1 - 8.
6. The expression (x^2 - 2x + 1) can be factored as (x - 1)^2.
7. Simplifying further, we have y = (x - 1)^2 - 9.
Therefore, the correct answer is A) (x - 1)^2 - 9. This is the vertex form of the given quadratic equation. The vertex of the parabola represented by this equation is (1, -9).