# What is the axis of symmetry and vertex for the graph  y=2x^2 -6x+1?

Apr 11, 2016

$V e r t e x \left(\frac{3}{2} , - \frac{7}{2}\right)$

#### Explanation:

x-coordinate of vertex, and axis of symmetry:
$x = - \frac{b}{2 a} = \frac{6}{4} = \frac{3}{2}$
y-coordinate of vertex:
$y \left(\frac{3}{2}\right) = 2 \left(\frac{9}{4}\right) - 6 \left(\frac{3}{2}\right) + 1 = \frac{18}{4} - \frac{18}{2} + 1 =$
$= - \frac{14}{4} = - \frac{7}{2}$
$V e r t e x \left(\frac{3}{2} , - \frac{7}{2}\right)$