1. **Problem statement:** A parabola intersects the x-axis at $x=3$ and $x=9$. We need to find the $x$-coordinate of the parabola's vertex. 2. **Formula and concept:** The parabola's roots (x-intercepts) are given as $x=3$ and $x=9$. The vertex of a parabola given by roots $r_1$ and $r_2$ lies exactly halfway between the roots on the x-axis. This is because the vertex is the axis of symmetry of the parabola. 3. **Calculate the midpoint:** The $x$-coordinate of the vertex is the average of the roots: $$x_{vertex} = \frac{r_1 + r_2}{2}$$ 4. **Substitute the values:** $$x_{vertex} = \frac{3 + 9}{2}$$ 5. **Simplify:** $$x_{vertex} = \frac{12}{2}$$ 6. **Final answer:** $$x_{vertex} = 6$$ The $x$-coordinate of the parabola's vertex is 6.