Question

chapter 1.6: type an equation for this absolute value function. *
1 point
type the equation in the form y = a|x − h| + k
copy/paste for absolute value bars: ||
(there is a graph of an absolute value function with grid lines, y-axis labeled with 5, 10, 15, x-axis labeled with -5, 0, 5, 10)

Explanation:

Step1: Identify vertex (h,k)

The vertex of the absolute value function is the lowest point on the graph, which is at $(1, 2)$. So $h=1$, $k=2$.

Step2: Substitute vertex into form

Substitute $h=1$, $k=2$ into $y=a|x-h|+k$:
$y=a|x-1|+2$

Step3: Solve for slope a

Use a second point on the graph, e.g., $(0,5)$. Substitute $x=0$, $y=5$:
$5=a|0-1|+2$
$5=a(1)+2$
$a=5-2=3$

Step4: Write final equation

Substitute $a=3$, $h=1$, $k=2$ into the form.

Answer:

$y=3|x-1|+2$