### Home > INT2 > Chapter 5 > Lesson 5.1.3 > Problem5-34

5-34.

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

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

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

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 $y\text{-coordinate}$ of the vertex. Then write the vertex as a point $(x,y)$.

Substitute the $x\text{-value}$ you found for $x$, and find the corresponding $y\text{-value}$.