What is the vertex form of # y = x(x-5)+13 #?

1 Answer
Jim G.
Apr 30, 2018

#y=(x-5/2)^2+27/4#

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"#

#y=x(x-5)+13=x^2-5x+13#

#y=x^2+2(-5/2)x+25/4-25/4+13#

#color(white)(y)=(x-5/2)^2+27/4larrcolor(red)"in vertex form"#

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