What is the vertex form of #y=2x^2 + 2x+6#?

1 Answer
Dec 30, 2017

#y=2(x+1/2)^2+11/2#

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 form use "color(blue)"completing the square"#

#• " the coefficient of the "x^2" term must be 1"#

#rArry=2(x^2+x+3)#

#• " add/subtract "(1/2"coefficient of the x-term")^2" to"#
#x^2+x#

#y=2(x^2+2(1/2)xcolor(red)(+1/4)color(red)(-1/4)+3)#

#rArry=2(x+1/2)^2+(2xx11/4)#

#rArry=2(x+1/2)^2+11/2larrcolor(red)"in vertex form"#