1. **State the problem:** We are given the function $h(x) = -4|x - 5|$ and need to understand its behavior. 2. **Formula and rules:** The function involves an absolute value, which means $|x - 5|$ is always non-negative. Multiplying by $-4$ will flip the graph vertically and scale it by 4. 3. **Intermediate work:** - The absolute value $|x - 5|$ measures the distance of $x$ from 5. - Multiplying by $-4$ means the output is always less than or equal to zero. 4. **Explanation:** - For $x = 5$, $h(5) = -4|5 - 5| = -4 imes 0 = 0$. - For $x > 5$, $h(x) = -4(x - 5)$, which decreases linearly as $x$ increases. - For $x < 5$, $h(x) = -4(5 - x)$, which also decreases linearly as $x$ moves away from 5. 5. **Summary:** The graph is a "V" shape flipped upside down with vertex at $(5,0)$, opening downward with slope magnitude 4 on both sides. **Final answer:** The function $h(x) = -4|x - 5|$ has vertex at $(5,0)$ and decreases linearly with slope $-4$ to the right and slope $4$ to the left of $x=5$.