What is the vertex form of #y=3x^2 -7x+5?

1 Answer
Jim G.
Jun 26, 2018

#y=3(x-7/6)^2+11/12#

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 "color(blue)"complete the square"#

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

#"factor out 3"#

#y=3(x^2-7/3x+5/3)#

#• " add/subtract "(1/2"coefficient of x-term")^2" to"#
#x^2-7/3x#

#y=3(x^2+2(-7/6)x color(red)(+49/36)color(red)(-49/36)+5/3)#

#color(white)(y)=3(x-7/6)^2+3(-49/36+5/3)#

#color(white)(y)=3(x-7/6)^2+11/12larrcolor(red)"in vertex form"#

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