#"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"#
#"to obtain this form use "color(blue)"completing the square"#
#• " the coefficient of the "x^2" term must be 1"#
#"factor out 9"#
#9(x^2-4/3x+4/9)=0#
#• " add/subtract "(1/2"coefficient of the x-term")^2" to"#
#x^2-4/3x#
#9(x^2+2(-2/3)xcolor(red)(+9/4)color(red)(-9/4)+9/4)=0#
#rArr9(x-2/3)^2+0=0#
#"the left side is now in "color(blue)"vertex form"#
#"with "h=2/3" and k=0#
#rArrcolor(magenta)"vertex "=(2/3,0)#
#"for intercepts solve the equation "#
#rArr9(x-2/3)^2=0#
#rArrx=2/3"( repeated)"#
#"this indicates a minimum at "(2/3,0)#
graph{9x^2-12x+4 [-10, 10, -5, 5]}
