How do you find the x and y intercepts for #y=(x+12)^2-144#?

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Answer 1 · 2016-12-05T04:06:55

The #x# intercepts are #(-24,0)# and #(0,0)#. The #y# intercept is #(0,0)#.

#y=(x+12)^2-144#

To find the #y# intercept, substitute #x=0# into the equation and solve for #y#.

#y=(0+12)^2-144#

#y=12^2-144#

#y=144-144#

#y=0#

The #y# intercept is the origin #(0,0)#.

It is also one of the #x# intercepts because #y=0# at this point.

To find the other #x# intercept, substitute #y=0# into the equation and solve for #x#.

#color(white)(aaa)0=(x+12)^2-144#
#+144=color(white)(aaaaaaa)+144color(white)(aaa)#Add 144 to both sides.

#144=(x+12)^2#

#sqrt144=sqrt[(x+12)^2]color(white)(aaa)#Square root both sides

#+-12=x+12#

#color(white)(a^2)12=x+12color(white)(aaa)-12=x+12#
#-12=color(white)(a)-12color(white)(aaa)-12=color(white)a-12#

#x=0color(white)(aaaaa)x=-24#

The #x# intercepts are #(-24,0)# and #(0,0)#.