What is the vertex form of #y= 4x^2+2x+12 #?

1 Answer
Jim G.
Feb 1, 2018

#y=4(x+1/4)^2+47/4#

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=4(x^2+1/2x+3)#

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

#y=4(x^2+2(1/4)xcolor(red)(+1/16)color(red)(-1/16)+3)#

#rArry=4(x+1/4)^2+4(-1/16+3)#

#rArry=4(x+1/4)^2+47/4larrcolor(red)"in vertex form"#

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