Question

which equation is represented by the graph below?
answer
\\( y = 5|x - 1| - 6 \\)
\\( y = 5|x - 1| + 6 \\)
\\( y = 5|x + 1| + 6 \\)
\\( y = 5|x + 1| - 6 \\)

Explanation:

Step1: Identify vertex form

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

Step2: Find vertex

From the graph, vertex is $(1, -6)$, so $h=1$, $k=-6$.

Step3: Determine slope $a$

Take a point on the graph, e.g., $(2, -1)$. Substitute into $y = a|x - 1| - 6$: $-1 = a|2 - 1| - 6 \Rightarrow -1 = a - 6 \Rightarrow a=5$.

Step4: Form equation

Substitute $a=5$, $h=1$, $k=-6$: $y = 5|x - 1| - 6$.

Answer:

y = 5|x - 1| - 6