#"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 constant.
#y-4=-(x-1)^2#
#"add 4 to both sides"#
#ycancel(-4)cancel(+4)=-(x-1)^2+4#
#rArry=-(x-1)^2+4larrcolor(red)" in vertex form"#
#"with " h=1" and " k=4#
#rArrcolor(magenta)"vertex "=(1,4)#
#color(blue)"Intercepts"#
#• " let x = 0, in equation for y-intercept"#
#• " let y = 0, in equation for x-intercepts"#
#x=0toy=-(0-1)^2+4=3larrcolor(red)" y- intercept"#
#y=0to-(x-1)^2+4=0#
#rArr-(x-1)^2=-4#
#"multiply both sides by - 1"#
#rArr(x-1)^2=4#
#color(blue)"take the square root of both sides"#
#sqrt((x-1)^2)=+-sqrt4larrcolor(red)" note plus or minus"#
#rArrx-1=+-2larr" add 1 to both sides"#
#rArrx=1+-2#
#rArrx=1-2=-1,x=1+2=3larrcolor(red)" x- intercepts"#
graph{-(x-1)^2+4 [-10, 10, -5, 5]}
