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

• Apr 14th 2012, 06:22 AM
strdatmage
which is an equation of the axis of symmetry of the graph of the equation y=x2-6x+2

which is an equation of the axis of symmetry of the graph of the equation y=x2-6x+2?
• Apr 14th 2012, 06:34 AM
Plato
Re: which is an equation of the axis of symmetry of the graph of the equation y=x2-6x
Quote:

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 $\displaystyle y=x^2-6x+2=(x-3)^2-7~?$
• Apr 14th 2012, 06:35 AM
earboth
Re: which is an equation of the axis of symmetry of the graph of the equation y=x2-6x
Quote:

Originally Posted by strdatmage

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:

$\displaystyle y=x^2-6x+2 = (x^2-6x \color{red}+ 9) - 9\color{black}+2= (x-3)^2-7$
• Apr 14th 2012, 07:05 AM
Soroban
Re: which is an equation of the axis of symmetry of the graph of the equation y=x2-6x
Hello, strdatmage!

Quote:

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

It is worthwhile to learn this formula . . .

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

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

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

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

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