"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"
rArry=-3(x^2-4x+8/3)
• " add/subtract "(1/2"coefficient of the x-term")^2" to"
x^2-4x
y=-3(x^2+2(-2)xcolor(red)(+4)color(red)(-4)+8/3)
color(white)(y)=-3(x-2)^2-3(-4+8/3)
rArry=-3(x-2)^2+4larrcolor(red)"in vertex form"
rArrcolor(magenta)"vertex "=(2,4)
"to find the intercepts"
• " let x = 0, in the equation for y-intercept"
• " let y = 0, in the equation for x-intercepts"
x=0toy=-3(-2)^2+4=-8larrcolor(red)"y-intercept"
y=0to-3(x-2)^2+4=0
rArr(x-2)^2=4/3
color(blue)"take square root of both sides"
x-2=+-sqrt(4/3)larrcolor(blue)"note plus or minus"
rArrx=2+-2/sqrt3
rArrx=2+-(2sqrt3)/3larrcolor(red)"x-intercepts"
