"we require to find the vertex and it's nature, that is"
"maximum or minimum"
"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 "-3
y=-3(x^2-x+2/3)
• " add/subtract "(1/2"coefficient of the x-term")^2" to"
x^2-x
y=-3(x^2+2(-1/2)xcolor(red)(+1/4)color(red)(-1/4)+2/3)
color(white)(y)=-3(x-1/2)^2-3(-1/4+2/3)
color(white)(y)=-3(x-1/2)^2-5/4larrcolor(red)"in vertex form"
rArrcolor(magenta)"vertex "=(1/2,-5/4)
"to determine if vertex is max/min"
• " if "a>0" then minimum "uuu
• " if "a<0" then maximum "nnn
"here "a=-3<0" hence maximum"
"range "y in(-oo,-5/4]
graph{-3x^2+3x-2 [-8.89, 8.89, -4.444, 4.445]}
