#"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"#
#"to obtain this form "color(blue)"complete the square"#
#y=x^2+2(4)xcolor(red)(+16)color(red)(-16)+14#
#rArry=(x+4)^2-2larrcolor(blue)"in vertex form"#
#rArrcolor(magenta)"vertex "=(-4,-2)#
#"to obtain the intercepts"#
#• " let x = 0, in the equation for y-intercept"#
#• " let y = 0, in the equation for x-intercept"#
#x=0rArry=0+0+14=14larrcolor(red)"y-intercept"#
#y=0rArr(x+4)^2-2=0larr"add 2 to both sides"#
#rArr(x+4)^2=2#
#color(blue)"take the square root of both sides"#
#sqrt((x+4)^2)=+-sqrt2larrcolor(blue)"note plus or minus"#
#rArrx+4=+-sqrt2larr"subtract 4 from both sides"#
#rArrx=-4+-sqrt2larrcolor(red)"exact values"#
graph{(y-x^2-8x-14)((x+4)^2+(y+2)^2-0.04)=0 [-10, 10, -5, 5]}
