Question

1 Without graphing, determine the characteristics of the graph.

(a) y = |x-3) -1

What is the vertex?

Answer 1

Answer: (3, -1)

Explanation:

y = |x-3|-1

When y=|x|, vertex is (0, 0).

Now, let's translate the graph so it becomes y = |x-3|-1.

|x| ==> |x-3| Translate the graph 3 units to the right

Vertex: (0+3, 0) ==> (3, 0)

|x-3| ==> |x-3|-1 Translate the graph 1 unit down

Vertex: (3, 0-1) ==> (3, -1)

Vertex: (3, -1)