Given the function $h\left(x\right) = 2\left(x + 3\right)^{2} + 2$:

1. What are the intercepts?

   Step 1(a):

   To find the y-intercept, substitute $0$ for $x$.

   $h\left(0\right) = −2\left(9\right) + 2$

   Step 2(a):

   To find the x-intercept substitute $0$ for $h\left(x\right)$.

   $0 = −2\left(x + 3\right)^{2} + 2$

   Step 3(a):

   $−2\left(x + 3\right)^{2} = −2$

   Step 4(a):

   $\left(x + 3\right)^{2} = 1$

   Step 5(a):

   $x + 3 = ± 1$

   Answer 1 (a):

   y-intercept$\left(0, −16\right)$

   Answer 2(a):

   x-intercept $\left(−4, 0\right), \left(−2, 0\right)$

2. What are the domain and range?