Which of the following is the x coordinates of a stationary point g(x)=9x^2-36x+35 ?
answers A, -5/3 B, 5/3 C, 2 D, 7/3 E, 4

Question

Which of the following is the x coordinates of a stationary point  g(x)=9x^2-36x+35 ?
answers   A, -5/3   B, 5/3   C, 2   D, 7/3   E, 4

Noah Atkinson · Accepted Answer

#x=2# #"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]}

Which of the following is the x coordinates of a stationary point g(x)=9x^2-36x+35 ? answers A, -5/3 B, 5/3 C, 2 D, 7/3 E, 4