#"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=-2(x-1)^2+3" is in vertex form"#

#"with "h=1" and "k=3#

#rArrcolor(magenta)"vertex "=(1,3)#

#"to find the intercepts"#

#• " let x = 0, in the equation for y-intercept"#

#• " let y= 0, in the equation for x-intercepts"#

#x=0rArry=-2(-1)^2+3=1larrcolor(red)"y-intercept"#

#y=0rArr-2(x-1)^2+3=0#

#"subtract 3 from both sides"#

#rArr-2(x-1)^2=-3#

#"divide both sides by "-2#

#rArr(x-1)^2=3/2#

#color(blue)"take the square root of both sides"#

#sqrt((x-1)^2)=+-sqrt(3/2)larrcolor(blue)"note plus or minus"#

#rArrx-1=+-sqrt3/sqrt2=+-1/2sqrt6#

#"add 1 to both sides"#

#rArrx=1+-1/2sqrt6larrcolor(red)"exact solutions"#

#x~~-0.22" to 2 dec. places ",x~~2.22larrcolor(red)"x-intercepts"#