Question

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

Answer 1

`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]}