What is the vertex form of #3y=(2x − 3)(x - 3) #?

1 Answer
Nov 23, 2017

#y=2/3(x-9/4)^2-3/8#

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 express "3y=(2x-3)(x-3)" in this form"#

#rArr3y=2x^2-9x+9#

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

#rArr3y=2(x^2-9/2x+9/2)#

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

#"to "x^2-9/2x#

#3y=2(x^2+2(-9/4)xcolor(red)(+81/16)color(red)(-81/16)+9/2)#

#color(white)(3y)=2(x-9/4)^2-9/8larrcolor(blue)"divide by 3"#

#rArry=2/3(x-9/4)^2-3/8larrcolor(red)"in vertex form"#