Question

write the absolute value functions for the graphs below

1. let b = 1
2. let b = 1

vertex: ________ h: k: vertex: ________
point: x: y: point:

Explanation:

Step1: Identify vertex (h,k)

The vertex of the absolute value graph is the corner point, which is at $(1, -2)$. So $h=1$, $k=-2$.

Step2: Use vertex form of abs function

The vertex form is $y = a|x - h| + k$. Substitute $h=1$, $k=-2$:
$y = a|x - 1| - 2$

Step3: Solve for a using a point

Pick a point on the graph, e.g., $(-1, 0)$. Substitute $x=-1$, $y=0$:
$0 = a|-1 - 1| - 2$
$0 = 2a - 2$
$2a = 2$
$a = 1$

Step4: Write final function

Substitute $a=1$, $h=1$, $k=-2$ into the vertex form.

Answer:

$y = |x - 1| - 2$
Vertex: $(1, -2)$
Point used: $(-1, 0)$
$h=1$, $k=-2$, $x=-1$, $y=0$