Question 72·Hard·Nonlinear Functions

When the quadratic function $g$ is graphed in the $xy$-plane, where $y = g(x)$, its vertex is $\left(\dfrac{5}{2},\,-9\right)$. One of the $x$-intercepts of this graph is $\left(\dfrac{11}{4},0\right)$. What is the other $x$-intercept of the graph?