Question

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

Answer 1

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(x^2 -6x +9)+5`
`y = 2x^2 -12x +18+5`

`y=2x^2 -12x +23`

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

Coordinate for `x`:

`(-(b)/(2a)) = (-12)/(2*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.