1. **State the problem:** We have two quadratic functions: $$f(x) = a(x - 3)^2 + 5$$ $$g(x) = a(x + 2)^2 - 1$$ We want to describe how the vertex of $g(x)$ is shifted relative to the vertex of $f(x)$ in terms of units left/right and up/down. 2. **Identify the vertices:** The vertex form of a quadratic function is: $$y = a(x - h)^2 + k$$ where $(h, k)$ is the vertex. - For $f(x)$, the vertex is at $(3, 5)$. - For $g(x)$, rewrite $g(x)$ as $a(x - (-2))^2 - 1$, so the vertex is at $(-2, -1)$. 3. **Calculate horizontal shift:** Horizontal shift = $x$-coordinate of $g$ vertex $-$ $x$-coordinate of $f$ vertex $$-2 - 3 = -5$$ A negative value means a shift to the left by 5 units. 4. **Calculate vertical shift:** Vertical shift = $y$-coordinate of $g$ vertex $-$ $y$-coordinate of $f$ vertex $$-1 - 5 = -6$$ A negative value means a shift down by 6 units. 5. **Final answer:** Compared to the graph of $f(x)$, the vertex for the graph of $g(x)$ has been shifted **5 units to the left**, and **6 units down**.