Question

Parent function help, attachment included. Thanks!

Answer 1

The answer should be B
The idea is that
\[
g(x) = (x+1)^2
\]
is like 2 functions..:
\[
\text{parent}(x) = x^2 \\
\text{son}(x) = x + 1 \\
g(x) = \text{parent}[\text{son}(x)] = \text{parent}(x+1) = (x+1)^2
\]
Now, since the parent is
\[
\text{parent}(x) = x^2 \\
\text{parent}(x) = 0 \\
x^2 = 0 \\
x = 0
\]
Parent parabola has its vertex on x=0
\[
g(x) = (x+1)^2 \\
g(x) = 0 \\
(x+1)^2 = 0 \\
x+1 = 0 \\
x = -1
\]
the parabola's vertex in here is x=-1, which is a shift to the left.

Answer 2

Thanks so much!! :)

Answer 3

sure np