# What is the axis of symmetry of the graph of y=2(x-3)^2+5?

May 14, 2015

The axis of symmetry is a line that divides the graphed function into identical parts - usually two.

First, let's just expand the function:

$y = 2 \left({x}^{2} - 6 x + 9\right) + 5$
$y = 2 {x}^{2} - 12 x + 18 + 5$

$y = 2 {x}^{2} - 12 x + 23$

Let's just find the coordinate for $x$ for our vertex:

Coordinate for $x$:

$\left(- \frac{b}{2 a}\right) = \frac{- 12}{2 \cdot 2} = - 3$

As we are dealing with a second degree function without restrictions to its continuity, we can infer that the function is symmetric both left and right the vertex. So, the line $x = 3$ is the axis of symmetry of this function.