What is the vertex form of #3y=-2(x+3)(x-1) #?

1 Answer

#(x--1)^2=-3/2(y-8/3)#

Explanation:

We start with the given
#3y=-2(x+3)(x-1)#

divide both sides of the equation by -2

#(3y)/(-2)=(-2(x+3)(x-1))/(-2)#

#(3y)/(-2)=(cancel(-2)(x+3)(x-1))/cancel(-2)#

#(3y)/(-2)=(x+3)(x-1)#

Expand the right sides of the equation by multiplication

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

complete the square

#-3/2y=x^2+2x+1-1-3#

#-3/2y=(x+1)^2-1-3#

#-3/2y=(x+1)^2-4#

transpose the -4 to the left side

#-3/2y+4=(x+1)^2#

factor out the -3/2 so that coefficient of y is 1 inside the grouping symbol

#-3/2(y-8/3)=(x--1)^2" " "#this is now the vertex form

God bless....I hope the explanation is useful.