1. **State the problem:** We are given the function $h(x) = -4|x - 5|$ and asked to understand its graph and properties. 2. **Formula and explanation:** The function involves the absolute value $|x - 5|$, which creates a V-shaped graph with vertex at $x=5$. 3. **Key points:** - The vertex is at $(5, 0)$ because $|x - 5|$ is zero when $x=5$. - The coefficient $-4$ outside the absolute value reflects the graph vertically (flips it upside down) and stretches it by a factor of 4. 4. **Graph behavior:** - For $x > 5$, $h(x) = -4(x - 5)$, a line with slope $-4$. - For $x < 5$, $h(x) = -4(5 - x) = 4(x - 5)$, a line with slope $4$. 5. **Intercepts:** - Vertex (also y-intercept for this shifted function) at $(5, 0)$. - To find the x-intercepts, set $h(x) = 0$: $$-4|x - 5| = 0 \implies |x - 5| = 0 \implies x = 5$$ 6. **Summary:** The graph is a downward-opening V with vertex at $(5,0)$, slopes $4$ and $-4$ on either side, and no other x-intercepts. **Final answer:** The function $h(x) = -4|x - 5|$ is a vertically stretched and reflected absolute value graph with vertex at $(5,0)$ and slopes $4$ (left) and $-4$ (right).