Question

below is the graph of $y = |x|$. translate it to make it the graph of $y = |x - 3| + 2$.

Explanation:

Step1: Analyze vertex of \( y = |x| \)

The vertex of \( y = |x| \) is at \( (0, 0) \).

Step2: Determine vertex of \( y = |x - 3| + 2 \)

For the absolute - value function \( y=a|x - h|+k \), the vertex is at \( (h,k) \). For \( y = |x - 3|+2 \), \( h = 3 \) and \( k = 2 \), so the vertex is at \( (3,2) \).

Step3: Find the translation vector

To get from the vertex \( (0,0) \) of \( y = |x| \) to the vertex \( (3,2) \) of \( y=|x - 3|+2 \), we need to move the graph 3 units to the right (since \( 3-0 = 3 \)) and 2 units up (since \( 2 - 0=2 \)). So we translate the graph of \( y = |x| \) 3 units to the right and 2 units up.

Answer:

Translate the graph of \( y = |x| \) 3 units to the right and 2 units up.