To find the x intercepts, plug in y = 0 and solve for x
y = (x+4)^2 - 9
0 = (x+4)^2 - 9 ... replace y with 0
9 = (x+4)^2
(x+4)^2 = 9
x+4 = plus/minus sqrt(9)
x+4 = sqrt(9) or x+4 = -sqrt(9)
x+4 = 3 or x+4 = -3
x = 3-4 or x = -3-4
x = -1 or x = -7
You have the correct answers. Nice work.
-----------------------------------------------------------------
Checking each answer:
Plug x = -1 into the original equation. You should get y = 0 as a result
y = (x+4)^2 - 9
y = (-1+4)^2 - 9
y = (3)^2 - 9
y = 9-9
y = 0 .... so this confirms x = -1 as a solution
The same should apply for the other potential solution x = -7
y = (x+4)^2 - 9
y = (-7+4)^2 - 9
y = (-3)^2 - 9
y = 9-9
y = 0 .... this confirms x = -7 as well
