"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 the method of "color(blue)"completing the square"
• " ensure the coefficient of the "x^2" term is 1"
rArrf(x)=-3(x^2-5/3x-3)
•" add/subtract "(1/2"coefficient of x-term")^2"to"
x^2-5/3x
f(x)=-3(x^2+2(-5/6)xcolor(red)(+25/36)color(red)(-25/36)-3)
color(white)(f(x))=-3(x-5/6)^2+133/12larrcolor(blue)"in vertex form"
rArrcolor(magenta)"vertex "=(5/6,133/12)
color(blue)"Intercepts"
• " let x = 0, in the equation for y-intercept"
• " let y = 0, in the equation for x-intercepts"
x=0toy=9larrcolor(red)"y-intercept"
y=0to-3(x-5/6)^2+133/12=0
rArr-3(x-5/6)^2=-133/12
rArr(x-5/6)^2=133/36
color(blue)"take the square root of both sides"
rArrx-5/6=+-sqrt(133/36)larrcolor(blue)"note plus or minus"
rArrx=5/6+-sqrt133/6larrcolor(red)"exact solutions"
rArrx~~-1.09" or "x~~2.76larrcolor(red)"x-intercepts"
