Final answer:
To translate the graph of f(x) = x^2 to create the graph of h(x) = -(x-1)^2 - 2, you need to apply two transformations: a horizontal translation and a vertical translation.
Step-by-step explanation:
To translate the graph of f(x) = x^2 to create the graph of h(x) = -(x-1)^2 - 2, we need to apply two transformations: a horizontal translation and a vertical translation. The horizontal translation, or shift, is determined by the value inside the parentheses, which in this case is (x-1). This means that the graph of h(x) will be shifted one unit to the right compared to the graph of f(x). The vertical translation is determined by the constant outside the parentheses, which is -2. This means that the graph of h(x) will be shifted two units downward compared to the graph of f(x).