Question

write the equation of the given parent graph. equation:

Explanation:

Step1: Identify the vertex

The vertex of the absolute - value - like graph is at the point $(9, 10)$. The general form of an absolute - value function is $y=a|x - h|+k$, where $(h,k)$ is the vertex. Here, $h = 9$ and $k = 10$.

Step2: Find the slope of one part of the graph

Taking the left - hand side of the graph, when $x=0$, $y = 1$. The slope from $(0,1)$ to $(9,10)$ is $m=\frac{10 - 1}{9-0}=1$. Since the graph opens upwards, $a = 1$.

Step3: Write the equation

Substitute $a = 1$, $h = 9$, and $k = 10$ into the general form $y=a|x - h|+k$. The equation is $y=|x - 9|+10$.

Answer:

$y=|x - 9|+10$