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

1 Answer
Guilherme N.
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(x^2 -6x +9)+5y=2(x2−6x+9)+5
y = 2x^2 -12x +18+5y=2x2−12x+18+5

y=2x^2 -12x +23y=2x2−12x+23

Let's just find the coordinate for xx for our vertex:

Coordinate for xx:

(-(b)/(2a)) = (-12)/(2*2) = -3(−b2a)=−122⋅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=3x=3 is the axis of symmetry of this function.

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