What is the vertex form of #y=3x^2 +10x - 8 #?

1 Answer
Jim G.
Dec 29, 2017

#y=3(x+5/3)^2-49/3#

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"#

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

#rArry=3(x^2+10/3x)-8#

#• " add/subtract "(1/2"coefficient of x-term")^2" to"#
#x^2+10/3x#

#rArry=3(x^2+2(5/3)xcolor(red)(+25/9)color(red)(-25/9))-8#

#color(white)(rArry)=3(x+5/3)^2-75/9-8#

#rArry=3(x+5/3)^2-49/3larrcolor(red)"in vertex form"#

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