#"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"#
#"the equation of the axis of symmetry is "x=h#
#"to obtain this form use "color(blue)"completing the square"#
#• " the coefficient of the "x^2" term must be 1"#
#rArry=-2(x^2+2x)-1#
#• " add/subtract "(1/2"coefficient of x-term")^2" to"#
#x^2+2x#
#y=-2(x^2+2(1)xcolor(red)(+1)color(red)-1))-1#
#color(white)(y)=-2(x+1)^2+2-1#
#color(white)(y)=-2(x+1)^2+1larrcolor(red)"in vertex form"#
#rArrcolor(magenta)"vertex "=(-1,1)#
#"equation of axis of symmetry is "x=-1#
#"to find the x-intercepts set y = 0"#
#rArr-2(x+1)^2+1=0#
#rArr(x+1)^2=1/2#
#rArrx+1=+-1/2=+-1/sqrt2#
#rArrx=-1+-1/sqrt2larrcolor(red)"exact values"#
#rArrx~~-1.71,x~~-0.29larrcolor(red)"x-intercepts"#
graph{(y+2x^2+4x+1)(y-1000x-1000)=0 [-10, 10, -5, 5]}
