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

2 Answers
Nov 13, 2017

Vetex is at #(3, 7)# and axis of symmetry is # x = 3 ; #

Explanation:

#y= -x^2+6x-2 or y= -(x^2-6x) - 2 # or

#y=-(x^2-6x+3^2)+9 -2 # or

#y=-(x-3)^2 + 7 # . This is vertex form of equation

#y=a(x-h)^2+k ; (h,k)# being vertex , here #h=3 ,k=7 #

Therefore vetex is at #(h,k) or (3, 7)#

Axis of symmetry is #x= h or x = 3 ; #

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

Nov 13, 2017

#x=3" and "(3,7)#

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]}