To find the equation for the translation so that the graph has the given vertex, we need to understand how the vertex affects the equation of the graph.
1. For the equation y = -|x| with a vertex (-5,0), we can observe that the absolute value function, |x|, always outputs a non-negative value. Therefore, to shift the graph of y = -|x| so that the vertex becomes (-5,0), we need to shift the graph horizontally 5 units to the right. The equation for the translation is y = -|x + 5|.
2. For the equation y = 2|x| with a vertex (-4,3), similarly, we can observe that the absolute value function, |x|, always outputs a non-negative value. To shift the graph of y = 2|x| so that the vertex becomes (-4,3), we need to shift the graph horizontally 4 units to the left. The equation for the translation is y = 2|x - 4| + 3. It seems like the answer in your book, y = 2|x| + 11, might be incorrect or based on a different interpretation of the question.
3. For the equation y = -|x| with a vertex (p,q), we need to find an equation that shifts the graph horizontally so that the vertex becomes (p,q). The equation for the translation is y = -|x - p| + q.
It is always a good idea to double-check with your teacher or consult additional resources to ensure the accuracy of answers provided in a book.