"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]}