Question

question
move at least one of the 9 guide points below to complete the graph of
y = |x - 3| + 2. moving the red points changes the vertical stretch or compression.
moving the blue point shifts the function left/right/up/down. click the buttons below
to start over or reflect over the x - axis.
reset reflect over x - axis

Explanation:

Step1: Identify vertex of $y=|x-3|+2$

The vertex of $y=|x-h|+k$ is $(h,k)$. Here, $h=3$, $k=2$, so vertex is $(3,2)$.

Step2: Adjust blue vertex point

Move the blue vertex point from (0,0) to (3,2).

Step3: Adjust red points

For $x < 3$: pick $x=-1$, $y=|-1-3|+2=6$ → (-1,6); $x=0$, $y=5$ → (0,5); $x=1$, $y=4$ → (1,4); $x=2$, $y=3$ → (2,3). For $x > 3$: $x=4$, $y=3$ → (4,3); $x=5$, $y=4$ → (5,4); $x=6$, $y=5$ → (6,5); $x=7$, $y=6$ → (7,6). Align red points to these coordinates. No vertical stretch/compression needed (coefficient of absolute value is 1).

Answer:

Move the vertex (blue point) from (0,0) to (3,2); keep red points aligned with $y = |x - 3| + 2$ (e.g., left of vertex: (-1,6), (0,5), (1,4), (2,3); right of vertex: (4,3), (5,4), (6,5), (7,6)).