"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]}