### Home > AC > Chapter 8 > Lesson 8.2.3 > Problem8-68

8-68.

The roots ($x$-intercepts) of $y = 2x^2 − 16x + 30$ are $(3,0)$ and $(5,0)$.

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

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

The $x$ coordinate of the vertex is halfway between $3$ and $5$.

$x = 4$

Substitute the vertex value of $x$ back into the original equation to find $y$.

$y = 2(4^²) − 16(4) + 30$

Solve for $y$.

$y = −2$

Coordinates $= (4, −2)$