For f(x) = |x - h| + k, the vertex is at which coordinates?

For f(x) = |x - h| + k, the vertex is at which coordinates?

• A. (k, h)
• B. (0, 0)
• C. (h, k)
• D. (h, -k)

Answer: (C)

The vertex appears where the inside of the absolute value is zero, since that’s where the graph reaches its lowest point before the vertical shift. For f(x) = |x - h| + k, set x - h = 0 to get x = h, and then f(h) = |0| + k = k. So the minimum point is at (h, k). Visually, |x| is a V with vertex at (0, 0); shifting right by h moves the vertex to (h, 0), and then up by k moves it to (h, k). That’s why the vertex is at (h, k). If you mix up the shifts, you’d describe a different graph, which doesn’t match this function.

The vertex appears where the inside of the absolute value is zero, since that’s where the graph reaches its lowest point before the vertical shift. For f(x) = |x - h| + k, set x - h = 0 to get x = h, and then f(h) = |0| + k = k. So the minimum point is at (h, k). Visually, |x| is a V with vertex at (0, 0); shifting right by h moves the vertex to (h, 0), and then up by k moves it to (h, k). That’s why the vertex is at (h, k). If you mix up the shifts, you’d describe a different graph, which doesn’t match this function.