# What is the axis of symmetry and vertex for the graph #y= -x^2 + 6x - 2#?

##### 2 Answers

**Vetex is at** **and axis of symmetry is**

#### Explanation:

Therefore vetex is at

Axis of symmetry is

graph{-x^2+6x-2 [-20, 20, -10, 10]} [Ans]

#### Explanation:

#"the equation of a parabola in "color(blue)"vertex form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#

#"where "(h,k)" are the coordinates of the vertex and a"#

#"is a multiplier"#

#• " if "a>0" then graph opens up"#

#• " if "a<0" then graph opens down"#

#"express y in vertex form using the method of "color(blue)"completing the square"#

#• " coefficient of "x^2" term must be 1"#

#rArry=-1(x^2-6x+2)#

#• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2-6x#

#rArry=-(x^2-6xcolor(red)(+9)color(red)(-9)+2)#

#color(white)(rArry)=-(x-3)^2+7larrcolor(red)"in vertex form"#

#rArrcolor(magenta)"vertex "=(3,7)#

#"since "a<0" then parabola is vertical and opens down"#

#"the axis of symmetry is vertical and passes through the"#

#"vertex with equation "x=3#

graph{(y+x^2-6x+2)(y-1000x+3000)((x-3)^2+(y-7)^2-0.05)=0 [-20, 20, -10, 10]}