1. **State the problem:** Find the focus and directrix of the parabola given by the equation $$(y + 2.5)^2 = 4(x - 4).$$ 2. **Identify the form:** This equation is in the form $$(y - k)^2 = 4p(x - h),$$ which represents a parabola that opens horizontally (left or right) with vertex at $$(h, k).$$ 3. **Find the vertex:** From the equation, the vertex is at $$(4, -2.5).$$ 4. **Determine $p$:** The coefficient $4p = 4$, so $$p = 1.$$ This means the parabola opens to the right (since $p > 0$). 5. **Find the focus:** The focus lies $$p$$ units to the right of the vertex along the x-axis, so $$\text{Focus} = (h + p, k) = (4 + 1, -2.5) = (5, -2.5).$$ 6. **Find the directrix:** The directrix is a vertical line $$p$$ units to the left of the vertex, so $$\text{Directrix}: x = h - p = 4 - 1 = 3.$$ **Final answer:** Focus at $$(5, -2.5)$$ and directrix $$x = 3.$$