Question

identify the equation for this graph.
$y = |x - 5| + 2$
$y = |x - 5| - 2$
$y = |x + 5| - 2$
$y = |x + 5| + 2$

Explanation:

Step1: Recall the vertex form of absolute value function

The general form of an absolute value function is \( y = |x - h| + k \), where \((h, k)\) is the vertex of the V - shaped graph.

Step2: Identify the vertex from the graph

Looking at the graph, the vertex (the point of the V) is at \((5, 2)\). So, \( h = 5 \) and \( k = 2 \).

Step3: Substitute h and k into the general form

Substituting \( h = 5 \) and \( k = 2 \) into \( y=|x - h|+k \), we get \( y = |x - 5|+2 \).

Answer:

\( y = |x - 5| + 2 \)