Question

write your answer in the form a|x - h| + k, where a, h, and k are integers or simplified fractions. g(x) =

Explanation:

Step1: Identify vertex (h,k)

The vertex of the absolute - value function is the point where the graph changes direction. From the graph, the vertex is at the point $(3,0)$, so $h = 3$ and $k=0$.

Step2: Find the value of a

We can use another point on the graph, say $(0,4)$. Substitute $x = 0$, $y = 4$, $h = 3$ and $k = 0$ into the equation $y=a|x - h|+k$. We get $4=a|0 - 3|+0$, which simplifies to $4 = 3a$. Solving for $a$, we have $a=\frac{4}{3}$.

Answer:

$g(x)=\frac{4}{3}|x - 3|+0=\frac{4}{3}|x - 3|$