What is the vertex form of # y = x^2 − 5x − 21 #?

1 Answer
Jim G.
Dec 17, 2017

#y=(x-5/2)^2-109/4#

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 the method of "color(blue)"completing the square"#

#• " ensure the coefficient of the "x^2" term is 1 which it is"#

#• " add/subtract "(1/2"coefficient of x-term")^2" to"#
#x^2-5x#

#y=x^2+2(-5/2)xcolor(red)(+25/4)color(red)(-25/4)-21#

#rArry=(x-5/2)^2-109/4larrcolor(red)"in vertex form"#

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