How do you find the x intercepts for #y - 2 = - | x + 3 | + 1#?

1 Answer
May 6, 2017

Answer:

#x=-6,x=0#

Explanation:

#"to find the x-intercepts"#

#• " let y = 0, in the equation"#

#y-2=-|x+3|+1#

#"add 2 to both sides"#

#ycancel(-2)cancel(+2)=-|x+3|+1+2#

#rArry=-|x+3|+3#

#y=0to-|x+3|+3=0#

#color(blue)"Isolate"" the absolute value"#

#rArr-|x+3|=-3#

#"multiply both sides by - 1"#

#rArr|x+3|=3#

#"there are 2 possible solutions to the equation"#

#rArrx+3=color(red)(+-)3#

#color(blue)"First solution"#

#x+3=color(red)(+)3#

#"subtract 3 from both sides"#

#rArrx=3-3=0larrcolor(magenta)" x-intercept"#

#color(blue)"Second solution"#

#x+3=color(red)(-)3#

#"subtract 3 from both sides"#

#rArrx=-6larrcolor(magenta)" x-intercept"#
graph{-|x+3|+3 [-10, 10, -5, 5]}