This is a quadratic expressed in terms of y instead of terms in x. Consequently the graph will be of shape type #sub# instead of type #nn#.

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#color(blue)("Manipulating the equation to give the required format")#

Given:#" "y^2+4y+3x-4=0#

#color(brown)("Subtract "3x" from both sides")#

#" "y^2+4y+0-4=-3x#

#color(brown)("Divide both sides by 3")#

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

#" "color(blue)(x=1/3y^2 +4/3y-4/3)# ........................(1)

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#color(blue)("Converting to Vertex Form")#

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

#color(brown)("Changing the structure into vertex form and jumping a")#

#color(brown)("number of steps.")#

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

But #k=-4/3# giving

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

#color(red)("If you need further explanation go to my profile page")# #color(red)("and leave me a message. You must also give me a link to this page.")#

Link #-># http://socratic.org/s/aszzseH6

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#color(green)("Observe that the plots of equation (1) and equation (2) coincide.")#

#color(green)("This demonstrates that they are the same thing but just look ")##color(green)("different!")#

Also notice the reversal of where you obtain the vertex coordinates

If the equation form had been y=... then you would have #y=-8/3# but in this case it is #x=-8/3# so also in this case #y=(-1)xx2=-2#

Vertex#" "->(x,y)" "-> (-8/3,-2)#