Question #97c8c
1 Answer
Sep 14, 2017
Explanation:
#"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 use the method of "color(blue)"completing the square"#
#• " ensure the coefficient of "x^2" term is 1"#
#rArry=-2(x^2-x-1)#
#• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2-x#
#y=-2(x^2+2(-1/2)xcolor(red)(+1/4)color(red)(-1/4)-1)#
#color(white)(y)=-2(x-1/2)^2+5/2larrcolor(red)" in vertex form"#
#rArrcolor(magenta)"vertex"=(1/2,5/2)#
#"when "x=6#
#y=-2(6-1/2)^2+5/2=-121/2+5/2=-58#
