1. The problem is to analyze and understand the function $$y = -3|x - 2| + 4$$ and its key features such as vertex and points. 2. The formula involves an absolute value function, which creates a V-shaped graph. The vertex form is $$y = a|x - h| + k$$ where $(h,k)$ is the vertex. 3. Here, $a = -3$, $h = 2$, and $k = 4$, so the vertex is at $(2,4)$. 4. The negative $a$ value means the graph opens downward (an upside-down V). 5. To find points, substitute $x$ values into the function: - For $x=2$: $$y = -3|2 - 2| + 4 = -3 \times 0 + 4 = 4$$ - For $x=1$: $$y = -3|1 - 2| + 4 = -3 \times 1 + 4 = 1$$ - For $x=0$: $$y = -3|0 - 2| + 4 = -3 \times 2 + 4 = -6 + 4 = -2$$ 6. The vertex and these points match the table given. 7. The graph is symmetric about the vertical line $x=2$. 8. The function decreases as $x$ moves away from 2 in either direction because of the negative coefficient. Final answer: The vertex is at $(2,4)$ and the graph is an upside-down V shaped by $y = -3|x - 2| + 4$ with points $(2,4)$, $(1,1)$, and $(0,-2)$.