"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]}
