How do you graph #x^ { 2} - 6x + 4= ( x - 3) ^ { 2} + y#?

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Answer 1 · 2018-03-18T01:36:03

The line is #y=-5#.

Expand the squared part, then see that some parts cancel out on both sides of the equation:

#x^2-6x+4=(x-3)^2+y#

#x^2-6x+4=(x-3)(x-3)+y#

#x^2-6x+4=x^2-3x-3x+9+y#

#x^2-6x+4=x^2-6x+9+y#

#color(red)cancelcolor(black)(x^2-6x)+4=color(red)cancelcolor(black)(x^2-6x)+9+y#

#4=9+y#

#4-9=y#

#-5=y#

#y=-5#

This equation is the horizontal line at the #y#-value #-5#. It looks like this:

graph{0x-5 [-10, 10, -10, 0]}