"the equation of a parabola in "color(blue)"vertex form" is.
•color(white)(x)y=a(x-h)^2+k
"where "(h,k)" are the coordinates of the vertex and a"
"is a multiplier"
"to obtain this form "color(blue)"complete the square"
y=-3(x^2-7/3x-4/3)
color(white)(y)=-3(x^2+2(-7/6)x+49/36-49/36-4/3)
color(white)(y)=-3(x-7/6)^2-3(-49/36-4/3)
color(white)(y)=-3(x-7/6)^2+97/12larrcolor(blue)"in vertex form"
color(magenta)"vertex "=(7/6,97/12)
"for y-intercept let x = 0"
y=4larrcolor(red)"y-intercept"
"for x-intercepts let y = 0"
-3(x-7/6)^2+97/12=0
-3(x-7/6)^2=-97/12
(x-7/6)^2=97/36
color(blue)"take the square root of both sides"
x-7/6=+-97/36larrcolor(blue)"note plus or minus"
"add "7/6" to both sides"
x=7/6+-sqrt97/6larrcolor(red)"exact values"
x~~-0.47,x~~2.81" to 2 dec. places"
