# Thread: which is an equation of the axis of symmetry of the graph of the equation y=x2-6x+2

1. ## which is an equation of the axis of symmetry of the graph of the equation y=x2-6x+2

Castle learning question

which is an equation of the axis of symmetry of the graph of the equation y=x2-6x+2?

2. ## Re: which is an equation of the axis of symmetry of the graph of the equation y=x2-6x

Originally Posted by strdatmage
which is an equation of the axis of symmetry of the graph of the equation y=x2-6x+2?
Did you draw the graph and look at it?
Is it true that $y=x^2-6x+2=(x-3)^2-7~?$

3. ## Re: which is an equation of the axis of symmetry of the graph of the equation y=x2-6x

Originally Posted by strdatmage
Castle learning question

which is an equation of the axis of symmetry of the graph of the equation y=x2-6x+2?
Your equation describes a parabola opening up. Thus the symmetry axis passes through the vertex of the parabola.

Complete the square and determine the x-coordinate of the vertex:

$y=x^2-6x+2 = (x^2-6x \color{red}+ 9) - 9\color{black}+2= (x-3)^2-7$

4. ## Re: which is an equation of the axis of symmetry of the graph of the equation y=x2-6x

Hello, strdatmage!

Which is an equation of the axis of symmetry of the graph of: . $y\:=\:x^2-6x+2\,?$

It is worthwhile to learn this formula . . .

For the parabola: $y \:=\:ax^2 + bx + c$
. . the axis of symmetry is: . $x \:=\:\frac{\text{-}b}{2a}$

[Think of the "front half" of the Quadratic Formula.]

In this problem: . $a = 1,\;b = \text{-}6,\;c = 2$

We have: . $x \:=\:\frac{\text{-}(\text{-}6)}{2(1)} \:=\:3$

The axis of symmetry is the vertical line: $x \,=\,3.$