1. **State the problem:** We need to graph the quadratic function $$f(x) = 8(x - 4)^2$$ in vertex form. 2. **Recall the vertex form of a quadratic function:** $$f(x) = a(x - h)^2 + k$$ where $(h, k)$ is the vertex of the parabola and $a$ determines the width and direction. 3. **Identify the vertex:** Here, $a = 8$, $h = 4$, and $k = 0$. So the vertex is at $(4, 0)$. 4. **Plot the vertex:** The point $(4, 0)$ is the lowest point on the graph since $a > 0$. 5. **Find another point:** Choose an $x$ value different from 4, for example $x = 5$. 6. **Calculate $f(5)$:** $$ f(5) = 8(5 - 4)^2 = 8(1)^2 = 8 $$ So the point $(5, 8)$ lies on the parabola. 7. **Plot the point $(5, 8)$:** This helps define the shape of the parabola. 8. **Sketch the parabola:** It opens upward, is narrow because $a = 8$ is large, and passes through the points $(4, 0)$ and $(5, 8)$. **Final answer:** The vertex is at $(4, 0)$ and the parabola passes through $(5, 8)$. The graph is of $$f(x) = 8(x - 4)^2$$.