1. **State the problem:** We need to analyze and understand the function $$y = -6 |x - 5|$$ and describe its graph. 2. **Recall the formula and properties:** The absolute value function $$|x - 5|$$ measures the distance of $$x$$ from 5 on the number line, so it is always non-negative. 3. The function $$y = -6 |x - 5|$$ takes the absolute value and multiplies it by -6, which means the graph will be a "V" shape reflected downward and stretched vertically by a factor of 6. 4. **Find the vertex:** The vertex occurs where the expression inside the absolute value is zero, i.e., when $$x - 5 = 0$$, so $$x = 5$$. 5. At $$x = 5$$, $$y = -6 |5 - 5| = -6 \times 0 = 0$$, so the vertex is at the point $$(5, 0)$$. 6. **Behavior on either side of the vertex:** - For $$x > 5$$, $$y = -6 (x - 5)$$ (since $$x - 5$$ is positive). - For $$x < 5$$, $$y = -6 (5 - x)$$ (since $$x - 5$$ is negative, absolute value flips the sign). 7. **Plot points:** - At $$x = 6$$, $$y = -6 |6 - 5| = -6 \times 1 = -6$$. - At $$x = 4$$, $$y = -6 |4 - 5| = -6 \times 1 = -6$$. 8. **Summary:** The graph is a "V" shape with vertex at $$(5,0)$$ opening downward, with slope -6 on the right side and slope 6 on the left side (because of the negative sign outside the absolute value). Final answer: The graph of $$y = -6 |x - 5|$$ is a downward opening "V" with vertex at $$(5,0)$$ and steepness factor 6.