What is the axis of symmetry and vertex for the graph #y=x^2-6x+8#?

1 Answer
Oct 9, 2017

#x=3" and "(3,-1)#

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"#

#"using the method of "color(blue)"completing the square"#

#• " ensure coefficient of "x^2" term is 1"#

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

#y=x^2+2(-3)xcolor(red)(+9)color(red)(-9)+8#

#color(white)(y)=(x-3)^2-1larrcolor(red)" in vertex form"#

#rArr"vertex "=(h,k)=(3,-1)#

#"the axis of symmetry is vertical and passes through"#
#"the vertex with equation"#

#x=3#
graph{(y-x^2+6x-8)(y-1000x+3000)=0 [-10, 10, -5, 5]}