"the equation of a parabola in "color(blue)"vertex form"the equation of a parabola in vertex form is.
•color(white)(x)y=a(x-h)^2+k∙xy=a(x−h)2+k
"where "(h,k)" are the coordinates of the vertex and a"where (h,k) are the coordinates of the vertex and a
"is a multiplier"is a multiplier
y=(x+3)^2+1" is in this form"y=(x+3)2+1 is in this form
color(magenta)"vertex "=(-3,1)vertex =(−3,1)
"let x=0, for y-intercept"let x=0, for y-intercept
y=9+1=10larrcolor(red)"y-intercept"y=9+1=10←y-intercept
"let y = 0, for x-intercepts"let y = 0, for x-intercepts
(x+3)^2+1=0(x+3)2+1=0
(x+3)^2=-1(x+3)2=−1
"this has no real solutions hence there are no"this has no real solutions hence there are no
"x-intercepts"x-intercepts
graph{(x+3)^2+1 [-20, 20, -10, 10]}
