What is the vertex form of #y=4x^2+x-4+10 #?

1 Answer
Jim G.
Nov 11, 2017

#y=4(x+1/8)^2+95/16#

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 express in this form use "color(blue)"completing the square"#

#y=4x^2+x+6#

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

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

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

#"to "x^2+1/4x#

#rArry=4(x^2+2(1/8)xcolor(red)(+1/64)color(red)(-1/64)+3/2)#

#color(white)(rArry)=4(x+1/8)^2+(4xx95/64)#

#color(white)(rArry)=4(x+1/8)^2+95/16#

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