Write an equation for the translation so the graph has the given vertex.
1. y=-|x| vertex (-5,0)
2. y=2|x| vertex (-4,3)
3. y=-|x| vertex (p,q)
I really have no idea how to even begin these, but I do know the answer to # 2 is y=2|x|+11 and #3 is
y=-|x-p|+q
Thanks in advance.
The vertex should be the lowest or highest point on the graph.
To shift left you add to x, so for 1. x+5 moves left 5 units and y=-|x+5| is the shift.
To shift up you add, so 2|x+4| shifts left 4 and y=2|x+4|+3. I don't see how you got y=2|x|+11 for this one.
#3 is y=-|x-p|+q looks correct.
Hmm, well that's what the answer is in my book.
This is what you told us:
2. y=2|x| vertex (-4,3); the answer to # 2 is y=2|x|+11
Do they want you to evaluate the point x=-4 or do a translation so the vertex is at (-4,3)? Check with your teacher, there could be a typo in the book. I really don't know how they got that answer.
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.