1. **State the problem:** We are given the quadratic function $$f(x) = \frac{3}{4}(x - 6)^2 + 2$$ and asked to plot the vertex and another point on the parabola. 2. **Identify the vertex:** The function is in vertex form $$f(x) = a(x - h)^2 + k$$ where the vertex is at $$(h, k)$$. Here, $a = \frac{3}{4}$, $h = 6$, and $k = 2$, so the vertex is at $$(6, 2)$$. 3. **Plot the vertex:** The vertex point is $$(6, 2)$$. 4. **Choose another point:** To find another point, pick an $x$-value different from 6, for example, $x = 7$. 5. **Calculate $f(7)$:** $$ f(7) = \frac{3}{4}(7 - 6)^2 + 2 = \frac{3}{4}(1)^2 + 2 = \frac{3}{4} + 2 = \frac{3}{4} + \frac{8}{4} = \frac{11}{4} = 2.75 $$ 6. **Plot the second point:** The point is $$(7, 2.75)$$. 7. **Summary:** The vertex is at $$(6, 2)$$ and another point on the parabola is at $$(7, 2.75)$$. This allows you to sketch the parabola accurately by plotting these points and drawing a smooth curve through them.