How do you find the vertex of the parabola #y=x^2+8x-19# by completing the square?

1 Answer
Jim G.
Oct 31, 2017

#(-4,-35)#

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"#

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

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

#y=x^2+8x-19larr" coefficient of "x^2" term is 1"#

#• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2+8x#

#y=x^2+2(4)xcolor(red)(+16)color(red)(-16)-19#

#color(white)(y)=(x+4)^2-35larrcolor(blue)"in vertex form"#

#"with "h=-4" and "k=-35#

#rArrcolor(magenta)"vertex "=(-4,-35)#

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