1. **State the problem:** We need to understand and graph the function $$y = \frac{5}{2} |x + 7|$$ and analyze how moving points affects the graph. 2. **Formula and explanation:** The function is an absolute value function with a vertical stretch factor of $$\frac{5}{2}$$ and a horizontal shift. The general form is $$y = a|x - h| + k$$ where: - $$a$$ controls vertical stretch/compression and reflection. - $$h$$ shifts the graph horizontally. - $$k$$ shifts the graph vertically. 3. **Identify parameters:** Here, $$a = \frac{5}{2}$$, $$h = -7$$ (since inside the absolute value is $$x + 7$$), and $$k = 0$$. 4. **Vertex location:** The vertex is at $$(-7, 0)$$ because the expression inside the absolute value is zero when $$x = -7$$. 5. **Effect of moving points:** - Moving the blue point (vertex) changes $$h$$ and/or $$k$$, shifting the graph left/right or up/down. - Moving red points changes the vertical stretch/compression factor $$a$$. 6. **Graph shape:** The graph is V-shaped with vertex at $$(-7, 0)$$ and arms extending upward with slope magnitude $$\frac{5}{2}$$. 7. **Summary:** - The vertex is at $$(-7, 0)$$. - The graph is vertically stretched by $$\frac{5}{2}$$. - Moving the blue point shifts the graph. - Moving red points changes the steepness. **Final answer:** The function $$y = \frac{5}{2} |x + 7|$$ has vertex at $$(-7, 0)$$ and vertical stretch factor $$\frac{5}{2}$$. Moving the blue point shifts the graph, moving red points changes the vertical stretch/compression.