The $x$-intercepts of the graph of $y=2x^2-16x+30$ are $\left(3,0\right)$ and $\left(5,0\right)$.  

1. What is the $x$-coordinate of the vertex? How do you know?

   Hint (a):

   Consider that the vertex of a parabola is on the line of symmetry.

   Answer (a):

   Since the line of symmetry lies exactly in the middle of the two $x\text{-intercepts}$, the $x\text{-coordinate}$of the vertex is $4$.

2. Use your answer to part (a) above to find the $y$-coordinate of the vertex. Then write the vertex as a point $\left(x,y\right)$.

   Hint (b):

   Substitute the $x$-value you found for $x$, and find the corresponding $y$-value.