1. The problem is to find values of $h$ and $k$ in the function $$y = |x - h| + k$$ so that the vertex of the "V" shape is at the point $(1,4)$. Then explore how to place the vertex anywhere on the plane. 2. The vertex of the absolute value function $y = |x - h| + k$ is at the point $(h, k)$ because the expression inside the absolute value is zero at $x = h$, and the value of $y$ at that point is $k$. 3. To get the vertex at $(1,4)$, set: $$h = 1$$ $$k = 4$$ 4. So the function becomes: $$y = |x - 1| + 4$$ 5. To place the vertex anywhere on the plane, simply choose any real numbers for $h$ and $k$. The vertex will be at $(h, k)$. 6. For example, if you want the vertex at $(a,b)$, then: $$h = a$$ $$k = b$$ 7. This shifts the graph horizontally by $h$ units and vertically by $k$ units. Final answer: $$y = |x - 1| + 4$$ has vertex at $(1,4)$. You can put the vertex anywhere by choosing $h$ and $k$ as the desired coordinates.