Question

write an absolute value equation for the graph shown to the right
y = (simplify your answer)

Explanation:

Step1: Identify vertex form of absolute - value function

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

Step2: Determine the vertex

From the graph, the vertex of the absolute - value function is $(3, - 4)$. So, $h = 3$ and $k=-4$, and the function becomes $y=a|x - 3|-4$.

Step3: Find the value of $a$

We can use another point on the graph, say $(2,-2)$. Substitute $x = 2$ and $y=-2$ into $y=a|x - 3|-4$.
\[

$$\begin{align*} -2&=a|2 - 3|-4\\ -2&=a|-1|-4\\ -2&=a - 4\\ a&=2 \end{align*}$$

\]

Answer:

$y = 2|x - 3|-4$