Question

chapter 1.6: type an equation for this absolute value function.
type the equation in the form y = a|x - h| + k
copy/paste for absolute value bars: ||
graph of an absolute value function with vertex at (1, 3), passing through (0, 2) and (4, 0) and (-2, 0)

Explanation:

Step1: Identify vertex (h,k)

The vertex of the absolute value function is the peak point at $(1, 3)$, so $h=1$, $k=3$.

Step2: Find slope a using a point

Use the y-intercept $(0,2)$. Substitute into $y=a|x-h|+k$:
$2 = a|0-1| + 3$
$2 = a(1) + 3$
$a = 2 - 3 = -1$

Step3: Substitute h,k,a into form

Plug $h=1$, $k=3$, $a=-1$ into $y=a|x-h|+k$.

Answer:

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