Question

write the absolute value functions for the graph be14. let b = 115. let b = vertex: k: vertex:point: point:

Explanation:

Step1: Recall absolute value form

The vertex form of an absolute value function is $y = a|x - h| + k$, where $(h,k)$ is the vertex.

Step2: Identify vertex from graph

From the graph, the vertex $(h,k)$ is $(1, -2)$. Substitute into the form:
$y = a|x - 1| - 2$

Step3: Use given point to find $a$

The graph passes through $(-4, 2)$. Substitute $x=-4, y=2$:
$2 = a|-4 - 1| - 2$
$2 = 5a - 2$

Step4: Solve for $a$

$5a = 2 + 2 = 4$
$a = \frac{4}{5}$

Step5: Write final function

Substitute $a=\frac{4}{5}$ back into the vertex form.

Answer:

$y = \frac{4}{5}|x - 1| - 2$