1. The problem is to understand and graph the function $y = 8 |x - 5|$. 2. This is an absolute value function with a vertical stretch factor of 8 and a horizontal shift of 5 units to the right. 3. The vertex of the graph is at the point where the expression inside the absolute value is zero, i.e., when $x - 5 = 0$ which gives $x = 5$. So the vertex is at $(5,0)$. 4. The function forms a "V" shape with the vertex at $(5,0)$. 5. The vertical stretch factor 8 means the graph is steeper than the basic $y = |x|$ graph. 6. To plot points, choose $x$ values around 5 and calculate $y$: - For $x=4$, $y = 8|4-5| = 8| -1| = 8$. - For $x=6$, $y = 8|6-5| = 8|1| = 8$. - For $x=3$, $y = 8|3-5| = 8| -2| = 16$. - For $x=7$, $y = 8|7-5| = 8|2| = 16$. 7. The graph is symmetric about the vertical line $x=5$. 8. The red points on the graph represent points on the lines $y = 8|x-5|$ at various $x$ values. 9. The blue point is the vertex at $(5,0)$, not $(1,0)$ as described in the prompt, which seems to be an error. 10. Moving the red points changes the vertical stretch or compression (the factor 8). 11. Moving the blue point shifts the function left/right/up/down, changing the vertex position. Final answer: The vertex is at $(5,0)$ and the graph is $y = 8|x-5|$ with vertical stretch 8 and horizontal shift 5 units right.