1. **State the problem:** We need to graph the function $$y = 5|x - 2| - 7$$ and identify its vertex. 2. **Recall the formula and rules:** The function is an absolute value function of the form $$y = a|x - h| + k$$ where: - $$a$$ controls the steepness and direction (positive means opening upwards) - $$(h, k)$$ is the vertex of the graph 3. **Identify the vertex:** From the function, $h = 2$ and $k = -7$, so the vertex is at the point $$(2, -7)$$. 4. **Plot the vertex:** This is the lowest point on the graph since $$a = 5 > 0$$. 5. **Find additional points:** Choose values of $$x$$ around 2 to find corresponding $$y$$ values. - For $$x = 1$$: $$y = 5|1 - 2| - 7 = 5| -1| - 7 = 5(1) - 7 = -2$$ - For $$x = 3$$: $$y = 5|3 - 2| - 7 = 5(1) - 7 = -2$$ 6. **Plot these points:** (1, -2) and (3, -2). 7. **Draw the graph:** Connect the points forming a "V" shape with vertex at $$(2, -7)$$ and arms rising steeply due to the factor 5. Final answer: The vertex is at $$(2, -7)$$ and the graph is a V-shaped absolute value function opening upwards with steepness 5.