#"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=(x-2)^2-3" is in this form"#
#"with " h=2,k=-3" and " a=1#
#rArrcolor(magenta)"vertex "=(2.-3)#
#color(blue)"shape of parabola"#
#• " if " a>0" then minimum turning point " uuu#
#• " if " a<0" then maximum turning point "nnn#
#"here "a=1rArr" minimum turning point"#
#color(blue)"Intercepts"#
#• " let x = 0, in equation for y-intercept"#
#• " let y = 0, in equation for x-intercepts"#
#x=0toy=(0-2)^2-3=1larrcolor(red)" y-intercept"#
#y=0to(x-2)^2-3=0#
#rArr(x-2)^2=3larr" take square root of both sides"#
#rArrx-2=+-sqrt3larr" note plus or minus"#
#rArrx=2+-sqrt3#
#x~~0.27,x~~3.73larrcolor(red)" x-intercepts"#
#color(blue)"Additional points"#
#"choose values for x and evaluate for y"#
#"Example"#
#x=-1toy=9-3=6rArr(-1,6)#
#x=4toy=4-3=1rArr(4,1)#
#"plot vertex, intercepts, additional points and draw a "#
#"smooth curve through them"#
graph{(x-2)^2-3 [-10, 10, -5, 5]}
