#"there are 2 possible approaches "#
#color(blue)"Algebraic ""or "color(blue)"Calculus"#
#"since the question is in Algebra"#
#"using the method of "color(blue)"completing the square"#
#• " ensure the coefficient of the "x^2" term is 1"#
#rArr9(x^2-4x)+35#
#• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2-4x#
#9(x^2+2(-2)xcolor(red)(+4)color(red)(-4))+35#
#=9(x-2)^2+35+(9xxcolor(red)(-4))#
#=9(x-2)^2-1larrcolor(red)"in vertex form"#
#"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"#
#rArrg(x)=9(x-2)^2-1" has a vertex at "(2,-1)#
#"the vertex- maximum or minimum is a stationary"#
#"point "#
#• " if "a<0" then stationary point is maximum "nnn#
#• " if "a>0" then stationary point is minimum " uuu#
#"here "a=9rArr" minimum stationary point"#
#rArr"x-coordinate of stationary point is "x=2#
graph{9x^2-36x+35 [-10, 10, -5, 5]}
