Question

what is the equation of the graph below? you can click the picture to zoom in!
$-|x - 2| + 4$
$y = -|x + 2| + 4$
$y = |x - 2| + 4$
$y = |x - 2| - 4$

Explanation:

Step1: Recall absolute value form

The parent absolute value function is $y=|x|$, with vertex at $(0,0)$. The transformed form is $y=a|x-h|+k$, where $(h,k)$ is the vertex, and $a$ determines direction/width.

Step2: Identify graph vertex

From the graph, the vertex (highest point) is at $(2, 4)$, so $h=2$, $k=4$.

Step3: Determine direction of opening

The graph opens downward, so $a=-1$ (negative coefficient flips the parent function).

Step4: Substitute values into form

Substitute $a=-1$, $h=2$, $k=4$ into $y=a|x-h|+k$:
$y = -|x-2| + 4$

Answer:

• $y=-|x-2|+4$