#"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.
#y=-3(x-2)^2+4" is in vertex form"#
#"with "(h,k)=(2,4)larrcolor(red)" vertex"#
#"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-3(x-2)^2=-4#
#rArr(x-2)^2=4/3#
#color(blue)"take the square root of both sides"#
#rArrx-2=+-sqrt(4/3)larr" note plus or minus"#
#rArrx=2+-2/sqrt3=2+(2sqrt3)/3#
#rArrx~~ 0.85" or "x~~ 3.15larrcolor(red)" x-intercepts"#
graph{-3(x-2)^2+4 [-10, 10, -5, 5]}
