Y = x ^ 2-6x + 7 in Scheitelpunktform?

#"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"#

#"given the parabola in "color(blue)"standard form";y=ax^2+bx+c#

#"then the x-coordinate of the vertex is"#

#•color(white)(x)x_(color(red)"vertex")=-b/(2a)#

#y=x^2-6x+7" is in standard form"#

#"with "a=1,b=-6" and "c=7#

#x_("vertex")=-(-6)/2=3#

#"substitute this value into the equation for y"#

#y_("vertex")=9-18+7=-2#

#(h,k)=(3,-2)#

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