What is the axis of symmetry and vertex for the graph #y=x^2-6x+8#?
1 Answer
Oct 9, 2017
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]}